I am a calc 2 student. And I stopped going to lectures cause I have no idea what that old fucken professor is talking about. Instead I go to the library and I look at your videos and try to understand the topic myself. Thanks a lot god bless you
Nick Merrick If you don't understand the lecture you'll fail the quiz so might as well just miss it too. I just missed the lecture and quiz days then went to take them after I learned it on my own. Thank God I graduated!!
On the last problem when you factored out the x^2 + 1/2 + 1/16x^2, your answer was( x+ 1/4x)^2. Why is his so? Because once I expanded ( x+ 1/4x)^2 I got x^2 + 1/2x^2 + 1/16 x^2
Seriously you are the BEST!! I love how you explain every little step, even if it is a small addition or subtraction step. And thank you for not having a condescending tone!!!!
I can't explain to you how great it is that you make good quality videos. I've been going over calculus 2 material since I am currently in that class. The way you explain is very straightforward and is helpful to watch right before an exam or starting my homework online.
Your videos are quick and concise, very easy to watch..and not too tedious. I happen to have a very good calc teacher, and adding the fact that I watch your video as review, this is making my math become extremely potent. Thanks Patrick.
My Calculus 2 professor faces the board and speaks in very broken English. You have clarified in 10 minutes what he spent 2 hours twisting into an indiscernible mess. Thank you.
Thank you so much for posting. Yesterday in class when the AP calc teacher went over this stuff, I had no idea what he was talking about. I didn't even know what arc length meant! Now, after watching this, the concept of it seems really simple and do-able. THANK YOU!!
Thank you so much for posting these, Its so helpful being able to see problems done where I can pause and go back if I need to to catch something. My recitation TA goes so fast through everything and skips lots of steps so I am in a constant state of confusion in class.
THANK YOU - I do IB and you have actually saved my maths internal assessment - I was trying to calculate the arcs of a basketball trajectory and I used parametric equations but it got weird because I had higher release angles getting shorter arcs - you're a legend, thank you
I have a calculus exam tomorrow and this will probably be on the test... really love how easy these videos are to understand because I simply cannot learn in my lecture. My professor basically turns her back to the class and talks to the whiteboard the entire time, but this is so much better for me! Thank you so much, hopefully I do well on my test tomorrow!
well, that is a circle of radius r, so you can use C = 2pi(r) (circumference formula) ... in this case, divide by 2 cause you only get the top half, so answer should be (pi)*(r)
Thanks a million for this video! I had a sub for my calc 1 class for this topic and he was awful. He taught it in an hours time with the proof and one example and I didn't understand a thing. He was basically a talking text book. Ten minutes of your video made this so simple to understand! Thanks!
My professor has a Phd in math, and I couldn't understand him! BUT YOU SIR! You explained extremely well that everything makes sense :') I am so glad you make these videos!! THANK YOU SO MUCH!!
You need to travel the world teaching college accredited courses. Most of us pay thousands in tution, yet still rely on your videos.... I wish the money i spent on tuition was in your pocket instead!!! Love and Light!
wish i had found you earlier! the semester is almost over and ive gone this whole time not understanding anything at all in calc 2, but this is clearing things up. will definitely have to use your videos as a resource for future math classes
Patrick You have no idea how much I love your videos... This is my second level of calculus and let me tell you, your played a huge role on my good grade in the first calculus level and for that thank you 😄😄 I will keep watching your videos...
Excellent video. I've been a fan for a year or so. Though when I watching it, I noticed that there is a useful trick when you go the 1/2's running around. -1/2 is the only number to which you can add 1 and it'll have the same absolute value (1/2). so (as 7:40 shows) if f '(x)^2 = [x - 1/(4x)]^2 = x^2 - 1/2 + 1/(16x^2) and f '(x)^2 +1 = x^2 + 1/2 + 1/(16x^2) you can automatically assume when factored it yields [x + 1/(4x)] (as 9:20 shows) as a consequence of factoring.
Almost our whole class (from UST) watches your videos! We certainly need help in integral calculus. Hope we all pass our class :) regards here from the Philippines!
@patrickJMT Awesome!!!! seriously you are better then my tutor and my teacher at explaining... well everything!! just calmed my nerves a bunch with this video about arc length. Thanks for your help man and congrats on the kick ass wife!
Thanks so much for your clear explanations! Just understanding that a key objective is to manipulate the expression under the root sign into a square assisted me greatly. You have a talent for teaching and your calm manner in solving this problem was appreciated. I hope you consider continuing on in online teaching much in the manner of Khan Academy; there is a real need out there (here) for online instruction and most do not have the technique down like yourself and Khan Academy... Thanks again!
@ace0415 for these type, you often end up factoring and doing some sort of u-sub. in general though, it could be quite difficult. but in a textbook, these problems are set up to work out
@lucypiao on a ti 84, there should be a MATH button. in that list there should be something like fnint(. click that. Then, type in the first function minus the second, x (make sure to use the commas between these things), and the limits of integration. So, figuring out the area beween curves x^2 and sqrt(x) between 0 and one would look something like fnInt(sqrt(x)-x^2,x,0,1) this shoud give your answer. You can use the function grapher to check which goes first.
@ 5:19 "It should always clearly um, always work out to be a positive number. So, if you get a negative number *sigh* Ssssomethings wrong..." Anyone else find the really humorous?
well actually when you take sqrt(u^2) you should write |u| anyway... It just so happens that both the functions he used in this video are positive for all values in the bounds.
Somewhat true... Textbooks have problems in them that are MUCH harder than most exam problems, but yes... he generally works easier problems in order to teach concepts.
Yeah textbook problems always seem to be harder than exam problems, with the basis being if you can do the homework in the book you wont have any problems with the exam itself.
he is taking the integral of (1/4x). So, we can say that (1/4) is a constant, so that is the same thing as (1/4) * the integral of (1/x). The integral of (1/x) is ln|x|, so the integral of (1/4x) is 1/4 ln |x|
@quiquemoranmoyano i have been reading a physics textbook at night (how nerdy, right?!). i understand the problems but still feel unqualified to do videos about it (cause i am unqualified!)
Couldn't you find the length just by taking the integral of f(x)-(f(x)-1)? Because that would give you the area between the line and the line one unit below it, so since area is l*w and width is 1, the area would equal the length.
On the last problem when you factored out the x^2 + 1/2 + 1/16x^2, your answer was( x+ 1/4x)^2. Why is his so? Because once I expanded ( x+ 1/4x)^2 I got x^2 + 1/2x^2 + 1/16 x^2
Hey Patrick, it's probably too late because you've made videos on everything, but do you think you could offer general steps in the description, or summarize at the end? You normally do a pretty good job of demonstrating but it's nice to have it lain out like that.
@ninjaturtle205 The fact that he's using hands and actually writing it down makes it so easier to understand. If he was like other videos where it is typed / computerized, it's very hard to follow!
Something I've noticed in a lot of problems I've worked out is that the final form is the same as the original and you insert the limits of integration... such as with the second problem you worked out, the original was y=(x^(2))+(ln(x)/4) and the end result was exactly this and you inserted 4 and 2 to get the numerical answer... is this usually what will happen when we don't have something like a Trig identity or lnx, or are there just certain ones that end up like this?
If it's a function of y, your dx after the integrand also should have been changed to a dy. You probably know that, just hard to get everything. Great videos.
thank you so much, it may sound whiney but my teacher is truly awful, doesn't explain a thing and expects us to read the stupid book...hey thanks again this is a god send man
How am I supposed to know that x^4+2x^2+1 is equal to (x^2+1)^2 ? I understand that it is the same thing... but I don't think I would've caught it on my own... is it just experience or is there a trick? - Thanks for all of your videos btw :D
You're such a good person. If I was old enough I'd buy you a beer, sir. A guy who takes time out of his day to help random people who need some extra help in Calc. #boss
I am a calc 2 student. And I stopped going to lectures cause I have no idea what that old fucken professor is talking about. Instead I go to the library and I look at your videos and try to understand the topic myself.
Thanks a lot god bless you
Kamel Ghouti I feels you. HAHA.. I wish I did that earlier.
+Kamel Ghouti dude i wish i could do that, my teacher has a ton of quizzes so i have to sit through an hour of lecture without learning anything
Nick Merrick If you don't understand the lecture you'll fail the quiz so might as well just miss it too. I just missed the lecture and quiz days then went to take them after I learned it on my own. Thank God I graduated!!
+Kamel Ghouti I'm doing the same too, I learn more from this videos since calculus I than with my professors :D
L bruh
Much respect to the creator of these videos.
+Josh Jeong thanks!
On the last problem when you factored out the x^2 + 1/2 + 1/16x^2, your answer was( x+ 1/4x)^2. Why is his so?
Because once I expanded ( x+ 1/4x)^2 I got x^2 + 1/2x^2 + 1/16 x^2
@@AliKayhan1 x^2 and 1/x^2 will get cancel in middle term
Seriously you are the BEST!! I love how you explain every little step, even if it is a small addition or subtraction step. And thank you for not having a condescending tone!!!!
I learned more from this 10 min video than my past 2 lectures that are over 2 hours long... thanks college!
Made a youtube account just so I can thank you for these videos. Thank you so much!
This is literally the question I have been stuck on for half an hour god bless you Patrick still saving uni kids 11 years later
I can't explain to you how great it is that you make good quality videos. I've been going over calculus 2 material since I am currently in that class. The way you explain is very straightforward and is helpful to watch right before an exam or starting my homework online.
Your videos are quick and concise, very easy to watch..and not too tedious. I happen to have a very good calc teacher, and adding the fact that I watch your video as review, this is making my math become extremely potent. Thanks Patrick.
My Calculus 2 professor faces the board and speaks in very broken English. You have clarified in 10 minutes what he spent 2 hours twisting into an indiscernible mess. Thank you.
Thank you so much for posting. Yesterday in class when the AP calc teacher went over this stuff, I had no idea what he was talking about. I didn't even know what arc length meant! Now, after watching this, the concept of it seems really simple and do-able. THANK YOU!!
Thank you so much for posting these, Its so helpful being able to see problems done where I can pause and go back if I need to to catch something. My recitation TA goes so fast through everything and skips lots of steps so I am in a constant state of confusion in class.
Thanks man! i missed class the day prof went over arc length. This has been a life saver, yet again! thanks!
THANK YOU - I do IB and you have actually saved my maths internal assessment - I was trying to calculate the arcs of a basketball trajectory and I used parametric equations but it got weird because I had higher release angles getting shorter arcs - you're a legend, thank you
I have a calculus exam tomorrow and this will probably be on the test... really love how easy these videos are to understand because I simply cannot learn in my lecture. My professor basically turns her back to the class and talks to the whiteboard the entire time, but this is so much better for me! Thank you so much, hopefully I do well on my test tomorrow!
I freaking love you, took me a while with my studying to figure out wtf the book was talking about and you just made it SIMPLE.....
You sir are the reason im passing Calc 2. Thnx soo much!!!!
Over a decade later and this dude is still saving peoples lives.
well, that is a circle of radius r, so you can use C = 2pi(r) (circumference formula) ... in this case, divide by 2 cause you only get the top half, so answer should be (pi)*(r)
Thanks a million for this video! I had a sub for my calc 1 class for this topic and he was awful. He taught it in an hours time with the proof and one example and I didn't understand a thing. He was basically a talking text book. Ten minutes of your video made this so simple to understand! Thanks!
thank you. i am taking calculas II online and your videos have helped me. you are now my new proffesor
My professor has a Phd in math, and I couldn't understand him! BUT YOU SIR! You explained extremely well that everything makes sense :') I am so glad you make these videos!! THANK YOU SO MUCH!!
"If you can't explain it simply, you don't understand it well enough."
Albert Einstein
You need to travel the world teaching college accredited courses. Most of us pay thousands in tution, yet still rely on your videos.... I wish the money i spent on tuition was in your pocket instead!!! Love and Light!
ha, i wish it was in my pocket too! :)
glad i could help though
I can never imagine my life without your videos. Thank you
been 14 years and it's still helpful
Thanks bro
wish i had found you earlier! the semester is almost over and ive gone this whole time not understanding anything at all in calc 2, but this is clearing things up. will definitely have to use your videos as a resource for future math classes
come back any time! :)
You are my one and only calculus teacher =}
Patrick
You have no idea how much I love your videos...
This is my second level of calculus and let me tell you, your played a huge role on my good grade in the first calculus level and for that thank you 😄😄
I will keep watching your videos...
Excellent video. I've been a fan for a year or so. Though when I watching it, I noticed that there is a useful trick when you go the 1/2's running around. -1/2 is the only number to which you can add 1 and it'll have the same absolute value (1/2). so (as 7:40 shows) if f '(x)^2 = [x - 1/(4x)]^2 = x^2 - 1/2 + 1/(16x^2) and f '(x)^2 +1 = x^2 + 1/2 + 1/(16x^2) you can automatically assume when factored it yields [x + 1/(4x)] (as 9:20 shows) as a consequence of factoring.
Almost our whole class (from UST) watches your videos! We certainly need help in integral calculus. Hope we all pass our class :) regards here from the Philippines!
@patrickJMT Awesome!!!! seriously you are better then my tutor and my teacher at explaining... well everything!! just calmed my nerves a bunch with this video about arc length. Thanks for your help man and congrats on the kick ass wife!
i dont know who you are. i just wanna say thank you so much. you are very helping me to finish my exam!!! it means TODAY!!!! Thank youuuuu!!!!!
Oh man I spent almost two hours on this question and I accidently found this video you just saved my life man you are officially my hero.
Thanks so much for your clear explanations! Just understanding that a key objective is to manipulate the expression under the root sign into a square assisted me greatly. You have a talent for teaching and your calm manner in solving this problem was appreciated. I hope you consider continuing on in online teaching much in the manner of Khan Academy; there is a real need out there (here) for online instruction and most do not have the technique down like yourself and Khan Academy... Thanks again!
the x's cancel when u multiply x by 1/4x giving you 1/4+1/4
@ace0415 for these type, you often end up factoring and doing some sort of u-sub. in general though, it could be quite difficult. but in a textbook, these problems are set up to work out
I always watch your videos before working on the new lessons for my online school on calculus. But today, my online teacher linked your vid hahaha
@lucypiao on a ti 84, there should be a MATH button. in that list there should be something like fnint(. click that. Then, type in the first function minus the second, x (make sure to use the commas between these things), and the limits of integration. So, figuring out the area beween curves x^2 and sqrt(x) between 0 and one would look something like fnInt(sqrt(x)-x^2,x,0,1) this shoud give your answer. You can use the function grapher to check which goes first.
Thank you especially for the part on factoring inside the radical.
I got a test tmrw and I’ve been studying for like 3 days on this and I just finally understood it!!
Words cannot express my gratitude. Thanks!!
@ 5:19
"It should always clearly um, always work out to be a positive number. So, if you get a negative number *sigh* Ssssomethings wrong..."
Anyone else find the really humorous?
well actually when you take sqrt(u^2) you should write |u| anyway...
It just so happens that both the functions he used in this video are positive for all values in the bounds.
Thank you so much! I had not idea how I was suppose to factor those terrible polynomials!
Thank you Patrick!!! God Bless you!
please try to do some more complicated problems
damn youre hardcore
Benjamin Jordan Exam problems usually are so much harder than any of textbook or Patirck videos problems
Somewhat true... Textbooks have problems in them that are MUCH harder than most exam problems, but yes... he generally works easier problems in order to teach concepts.
Yeah textbook problems always seem to be harder than exam problems, with the basis being if you can do the homework in the book you wont have any problems with the exam itself.
KFUPM XD
second semester typically
Thank you for taking time out of your day to do these videos. :)
he is taking the integral of (1/4x). So, we can say that (1/4) is a constant, so that is the same thing as (1/4) * the integral of (1/x). The integral of (1/x) is ln|x|, so the integral of (1/4x) is 1/4 ln |x|
@quiquemoranmoyano i have been reading a physics textbook at night (how nerdy, right?!). i understand the problems but still feel unqualified to do videos about it (cause i am unqualified!)
Thank you! YOU SHOULD WRITE A CALC BOOK!
My Calc book confused me much. I'm so glad I watched your video!
Did u forget to add the plus one after plugging in the [f'(x)]^2 into the L formula?
when you change the limits to the values of y, dx should be replaced by dy as well.
I agree
You make engineering math easy. Thank you.
Funny enough, this was one of my homework problems. The exact same
You did that in exactly 10 minutes you absolute legend
the first question just came in my calculus exam. Exactly the same numbers !!
glad you like my videos :) spread the word!
thanks! you are a god of calculus patrick
You, sir, helped me pass an exam. Thank you!
Very well designed example. Extremely useful video.
Couldn't you find the length just by taking the integral of f(x)-(f(x)-1)? Because that would give you the area between the line and the line one unit below it, so since area is l*w and width is 1, the area would equal the length.
On the last problem when you factored out the x^2 + 1/2 + 1/16x^2, your answer was( x+ 1/4x)^2. Why is his so?
Because once I expanded ( x+ 1/4x)^2 I got x^2 + 1/2x^2 + 1/16 x^2
(x*1/4x)+(x*1/4x)=(x/4x)+(x/4x)=(1/4)+(1/4)
x multiplied by 1/4x would allow you to cancel out the x values and leave you with 1/4.
Hey Patrick, it's probably too late because you've made videos on everything, but do you think you could offer general steps in the description, or summarize at the end? You normally do a pretty good job of demonstrating but it's nice to have it lain out like that.
Great videos to watch to prepare for lecture... Or the night before the exam! Either way the vids are great!
Yes those 2006 videos are helping me.
My friend, you are the best patrickJMT! thanks again, very very helpful. Now, if you only taught physics!
You are a life savor
thank you for doing these tutorials
and i hope you continue :)
honestly, you have videos for everything i need! you rock :)
patrick, Thanks to you. I passed math easily, I think you are talented about that explain something mathematically. Thanks from TURKEY :)
Thanks again Patrick
@ninjaturtle205 The fact that he's using hands and actually writing it down makes it so easier to understand. If he was like other videos where it is typed / computerized, it's very hard to follow!
Dude, you're saving me for my Calculus exam! Appreciated :D
i love you patrick for doing the exact same math problem that was in my hw!!!
Damn thank you SOOOO much, for tat last example I didn't notice that perfect square.
wow THANKS A LOT
your videos are always so informative
better than my professor
Oh Patrick, you are my hero.
Do you teach? If so what school?
I would love to send them an email, and tell them how amazing of a teacher you are.
Something I've noticed in a lot of problems I've worked out is that the final form is the same as the original and you insert the limits of integration... such as with the second problem you worked out, the original was y=(x^(2))+(ln(x)/4) and the end result was exactly this and you inserted 4 and 2 to get the numerical answer... is this usually what will happen when we don't have something like a Trig identity or lnx, or are there just certain ones that end up like this?
You Sir, are awesome.
I love your videos!
If it's a function of y, your dx after the integrand also should have been changed to a dy. You probably know that, just hard to get everything. Great videos.
I agree
Taking cal 3 right now. Wish I found you sooner!
thank you so much, it may sound whiney but my teacher is truly awful, doesn't explain a thing and expects us to read the stupid book...hey thanks again this is a god send man
How am I supposed to know that x^4+2x^2+1 is equal to (x^2+1)^2 ? I understand that it is the same thing... but I don't think I would've caught it on my own... is it just experience or is there a trick? - Thanks for all of your videos btw :D
Wow, you made me feel so smart watching this because I could actually follow along, you're really good, thanks! :)
@ninjaturtle205 cause i do not want to.
Thank you so much for these videos, they are very helpful!
Thank you! I just had a problem like example 2 in class today and was kinda confused about how you got the squared function. :P
glad i am able to help : )
I feel like going to my lecture is a waste. I learned more in this 10 min videos than a two hr lecture that included a derivation of the formula.
one question. will they always provide you the limits of integration? and if they dont how would you find them?
1/2*2 = 1 so it goes away and ur just left with x
Dude! I love you! (and I mean that in the manliest way possible). Thank you for continuously saving my bacon.
Good work. Opened me up.
Thank alot
You're such a good person. If I was old enough I'd buy you a beer, sir. A guy who takes time out of his day to help random people who need some extra help in Calc.
#boss
If you got a negative number....Something is wrong.
HA!
Thanks a lot man, I really hope I become a Professor like you do!
Thank you Patrick
when u multiply out (x+1/4x)(x+1/4x), doesn't that leave u with a 1/2 x^2 instead?
2nd year Electrical undergrad from MAPUA Institute of Technology here!
i doubt i will ever hire people in dallas/fort worth...sorry!
Thanks this really helped me out
thanks a lot sir. It's truly important for me