Only 40,000 views? that shows how very few people take math seriously. I am thankful for patrickJMT because he makes this blurry vision of Calculus a lot clearer.
hope this doesn't come off as weird, but you are one of the most intelligent individuals in the world because of your ability to teach difficult concepts to others in an effortless manner. you were born to do this.
+Juan Vera I agree there are a lot of smart people when it comes to math or anything in general but the question is can they teach so the student can understand.
True but i think its all about the speed of how people teach? Everyone is learns different. But sometimes teacher dont realise they need to teach at a slow pace so everyone can understand. My teacher would do this problem in a minute and i would be clueless lol
Extremely beneficial. I have been terrified all week about my upcoming test because I have no idea what my teacher is talking about 95% of the time. These videos have definitely clarified what my book and teacher cannot. Thanks!
you have literally saved my academic career. my calc professor is great, but teaches at ungodly speeds during his lectures. you have slowed everything down and have pretty much answered all of my questions about pretty much everything up to this point. just wanted to say thanks haha
thank you very much , you've helped me a lot , i'm from Saudi Arabia and my teacher doesn't revise with us before exams , but from now on , i think i don't need him any more .
YOU MAKE FEEL LIKE A MATH GENIUS! which I'm not but that tells a lot about YOU rather than me! You're the best Patrick. wouldn't have gone through first year engineering maths without you.
THANKS SO MUCH! THIS LITERALLY SAVED MY LIFE. I have a Exam tomorrow and had no idea what to do after using the double angle formula once. Thx again!!!!
yes. So long as it is something that you can factor out of the entire piece that you are integrating: for example, you can take the integral of int (5x^2.+5x)dx = 5*int(x^2+x)dx It's kind of like taking out a common factor (so long as there is no variable in which you factor out, because you need to integrate the variable). Sometimes this helps you, and in some cases it doesn't.
Thanks a lot Patrick, I really appreciate your help on everything man. The way you explain this stuff is so clear. Other professors make this stuff that's supposed to really be as easy as you show it, hard as hell!! Thanks again bro and I will keep watching your great videos
A big thanks for the time to supply these vids. These and your site have been extremely helpful. Only -ve comment is the distortion when you speak to loud into your mic.
After watching your videos I have one major and serious regret---I regret not knowing about your videos my freshman year of college. If I would have, I would've done a lot better. You're a perfect teacher. Thankfully I have your videos at my disposal entering my sophomore year. God Bless
I'm doing practice for an upcoming exam so I stopped the video just as you identified the problem here and worked it through. I got the same answer as you, but in seemingly far fewer steps.. I basically put parentheses around the entire sinxcosx expression and squared the entire thing (sinxcosx)^2 and from there used the double angle identity of sin2x/2 in its place. Squaring that gave me sin^2(2x)/4, pulled the 1/4 out and converted the sin^2(2x) to 1/2(1-cos(4x). Multiplied the 1/2 through and then took the integral. No need to foil anything. Guess there's always more than one or two ways to skin these kinds of cats. :)
Great video, your trig integral videos have been a big help! For this particular problem though i found it much less tedious to just rewrite (Sinx)^2(Cosx)^2 as (SinxCosx)^2 and then use the identity: SinxCosx = 1/2Sin2x And because we have (SinxCosx)^2 that would equal 1/4(Sin2x)^2. Then use u-substitution for 2x and just integrate 1/8(Sinu)^2. But thats just what i wouldve done. I guess i try to avoid the other identity that you used because i find it can make things messy sometimes lol thanks again!
My Russian professor went over this today. He doesnt smile. And he never understands our questions. You are so much easier to understand and follow. He spent about 25 minutes on an even powers trig integral problem, where you did it in
Patrick, all I can say is THANK YOU SOOOO MUCH!!!!!! I'm not joking, you are a great teacher. Calculus is hard, and trig. sub. is even harder, but you make it seem simple and straightforward. Thanks again :) ps. would you be make more videos? I think everyone would love that. :)
@entrevu here is a easy way to remember the derivatives just know these 2. 1. sin -> cos 2. cos-> -sin now you know that, just change the signs for the other ones: 3. -sin->-cos 4. -cos->sin now when you want to do anti-derivative, just go backwards, so anti-derivative of cos x is sin x according to rule 1
yes, there is some identity you can use to speed this up. i know this works though, so i have never bothered to think about it anymore : ) however, feel free to play with is and get back with me! : ) as erdos would tell you: this is a $1 question
yea, i agree the audio in a few sucks. i think i have that fixed now, and it should not be a problem in any more of my future videos. i am learning the technical side of production making these videos : )
thank you so much,now it will be easy for me to finish my homework... at 5:28 why at the second step written 1/2 dx...then later at the next step it became 1/2x.... but seriously this video help me a lot.thank u =)
It'd be easier to express the sin^2(x)cos^2(x) as (sin(x)cos(x))^2 and then use the identity [sin(2x)=2sin(x)cos(x) i.e. sin(x)cos(x)=1/2*sin(2x)] to convert it to 1/4*sin^2(2x) then change that into 1/8*(1-cos(4x)) and proceed to integrate from there. Saves 4 steps.
@patrickJMT there's an easier way of solving this. You could just write the square of sin2x divided by 4 in the beginning instead of using the other formula :)
Think of dx not just as dx, but as 1*dx. the integral of 1 is x that is where the x is coming from. If that doesn't help, think of the derivative of x, it is just 1. The integral is just the reverse of a derivative, so the (1/2)*integral(1*dx) must be (1/2)*x
thank you for the video patrick.. but i gotta ask.. in different trigonometric techniques of intergration. aren't we suppose to use by parts instead of U substitution?
I have a question. In your first problem of this video you have the integral of (sin^2x)(cos^2x) and I get how you did all that, but my book has the same question but instead its the integral of 16(sin^2x)(cos^2x) and they get an answer thats way off and includes cos^3x. Wouldn't you just take out the 16 and distribute it at the end? How does that change the final answer?
Patrick, you are a wonderful human being. Thank you so much for your contributions to the mathematically challenged!
You are a gift to all of us who need your wise teachings amongst a barren idiotic world.
+Brittany Loafman glad i could help you out :)
Belle Eden we can integrate bad guys to death now XD
glad i was able to help : )
I was in tears until I started watching your videos. thank you
A hero of students who goes to youtube instead of listening to their teachers. :D I'll give you a medal for that Patrick!
Safe to say, best, easiest to understand maths tutes online. Gone from barely passing to aceing maths.
Cheers mate.
Only 40,000 views? that shows how very few people take math seriously. I am thankful for patrickJMT because he makes this blurry vision of Calculus a lot clearer.
hope this doesn't come off as weird, but you are one of the most intelligent individuals in the world because of your ability to teach difficult concepts to others in an effortless manner. you were born to do this.
+Juan Vera I agree there are a lot of smart people when it comes to math or anything in general but the question is can they teach so the student can understand.
True but i think its all about the speed of how people teach? Everyone is learns different. But sometimes teacher dont realise they need to teach at a slow pace so everyone can understand. My teacher would do this problem in a minute and i would be clueless lol
its weird that u thought that was a weird thing to say
Extremely beneficial. I have been terrified all week about my upcoming test because I have no idea what my teacher is talking about 95% of the time. These videos have definitely clarified what my book and teacher cannot. Thanks!
you have literally saved my academic career. my calc professor is great, but teaches at ungodly speeds during his lectures. you have slowed everything down and have pretty much answered all of my questions about pretty much everything up to this point. just wanted to say thanks haha
thank you very much , you've helped me a lot , i'm from Saudi Arabia and my teacher doesn't revise with us before exams , but from now on , i think i don't need him any more .
YOU MAKE FEEL LIKE A MATH GENIUS! which I'm not but that tells a lot about YOU rather than me! You're the best Patrick. wouldn't have gone through first year engineering maths without you.
14y ago vid and nowadays teachers not doing this topic. You are only saviour here
THANKS SO MUCH! THIS LITERALLY SAVED MY LIFE. I have a Exam tomorrow and had no idea what to do after using the double angle formula once. Thx again!!!!
yes. So long as it is something that you can factor out of the entire piece that you are integrating: for example, you can take the integral of int (5x^2.+5x)dx = 5*int(x^2+x)dx
It's kind of like taking out a common factor (so long as there is no variable in which you factor out, because you need to integrate the variable). Sometimes this helps you, and in some cases it doesn't.
Thanks a lot Patrick, I really appreciate your help on everything man. The way you explain this stuff is so clear. Other professors make this stuff that's supposed to really be as easy as you show it, hard as hell!! Thanks again bro and I will keep watching your great videos
Professor Patrick, your teaching is godlike!
A big thanks for the time to supply these vids. These and your site have been extremely helpful. Only -ve comment is the distortion when you speak to loud into your mic.
After watching your videos I have one major and serious regret---I regret not knowing about your videos my freshman year of college. If I would have, I would've done a lot better. You're a perfect teacher. Thankfully I have your videos at my disposal entering my sophomore year. God Bless
I'm doing practice for an upcoming exam so I stopped the video just as you identified the problem here and worked it through. I got the same answer as you, but in seemingly far fewer steps.. I basically put parentheses around the entire sinxcosx expression and squared the entire thing (sinxcosx)^2 and from there used the double angle identity of sin2x/2 in its place. Squaring that gave me sin^2(2x)/4, pulled the 1/4 out and converted the sin^2(2x) to 1/2(1-cos(4x). Multiplied the 1/2 through and then took the integral. No need to foil anything. Guess there's always more than one or two ways to skin these kinds of cats. :)
Patrick you got me through calc 1 and im still relying on you for calc two so please dont stop making these videos they are so damn helpfull.
Great video, your trig integral videos have been a big help! For this particular problem though i found it much less tedious to just rewrite (Sinx)^2(Cosx)^2 as (SinxCosx)^2 and then use the identity:
SinxCosx = 1/2Sin2x
And because we have (SinxCosx)^2 that would equal 1/4(Sin2x)^2. Then use u-substitution for 2x and just integrate 1/8(Sinu)^2. But thats just what i wouldve done. I guess i try to avoid the other identity that you used because i find it can make things messy sometimes lol thanks again!
My Russian professor went over this today. He doesnt smile. And he never understands our questions. You are so much easier to understand and follow. He spent about 25 minutes on an even powers trig integral problem, where you did it in
these videos have seriously been a life saver, thank you
I have a calc 2 test next week and this is so helpful, thank you!! I couldnt even math before this 😭😭
u deserve money. lots. i pay this school so much but you teach it better.
Patrick, the math maker. I am glad I met you. Oh, yes, thanks a million.
Patrick, all I can say is THANK YOU SOOOO MUCH!!!!!!
I'm not joking, you are a great teacher. Calculus is hard, and trig. sub. is even harder, but you make it seem simple and straightforward.
Thanks again :)
ps. would you be make more videos? I think everyone would love that. :)
@Sarah Hudak The formula is for cos^2x but the term in the red bracket is cos^2(2x). The coefficients get multiplied. 2*2, hence the 4x.
@entrevu
here is a easy way to remember the derivatives
just know these 2.
1. sin -> cos
2. cos-> -sin
now you know that, just change the signs for the other ones:
3. -sin->-cos
4. -cos->sin
now when you want to do anti-derivative, just go backwards, so anti-derivative of cos x is sin x according to rule 1
You are the reason I am getting through engineering haha
Same idea bro
HAHAHAHAHA. Hope we could make it to the last!
Did you make it?
Did you make it through?
Tyler Miller years have passed. How did things go?
yes, there is some identity you can use to speed this up. i know this works though, so i have never bothered to think about it anymore
: ) however, feel free to play with is and get back with me! : ) as erdos would tell you: this is a $1 question
I have a calc 2 exam later today, this video just saved me!!!!
It's not always that the professor is bad, it's that Patrick is just so good.
best tutor eveerr, you actually take the time unlike professors
all of it. it was all relative to what i understood up to that point. eventually it gets beyond what i can understand
the foil can be excluded because of the algebra
a^2-b^2 = (a+b)(a-b)
so
instantly,we knew it'd be 1-cos^2(2x).
great work! =]
It was so long way to find it,you can find it simply without using u substitution,but thank you,your videos so helpful))
yea, i agree the audio in a few sucks.
i think i have that fixed now, and it should not be a problem in any more of my future videos.
i am learning the technical side of production making these videos : )
THANKS!!!!! You explain very well and your website is way better then khanacademy :D
thank you so much,now it will be easy for me to finish my homework...
at 5:28 why at the second step written 1/2 dx...then later at the next step it became 1/2x....
but seriously this video help me a lot.thank u =)
Thank you man. I needed this so badly.
This is incredible. Thanks so much and God bless!
i really thankful that you have a video like this it really helps!=)
*.* you just explained in 2 minutes what i have not been able to understand for a day and a half, I hope UA-cam has made you a partner and pays you
thank you for sharing your knowledge in calculus
how are there only 17000 views, it's the greatest!
glad i could help. and : key lime or buttermilk would be great.
Thank you, you make it simple.
i will go with 209 cause that number is bigger.
u re really helpful u ve made it easier for me.. thank u so much.
Patrick you are the best!!!
umaiththa,you are the best
you helped me out better than my prof did
this is soo much clear than my professor. All I see is her back blocking the problem while she's trying to solve/teach it...
Great video man! you be left handed is a real bummer though. It's hard to take notes after you.
Thanks a lot this really helps.
ok, i added the tags :)
youtube is made for patrickJMT!!
UBER THANKS DUDE! :))
U-substitution when integrating cos(4x) isant needed it would just be sin(4x)/4 because of the chain rule.
whoa! thanks to your vids. i able to pass last 2 exams in calculus 2 because of our vids. thanks alot. haha.XD
It'd be easier to express the sin^2(x)cos^2(x) as (sin(x)cos(x))^2 and then use the identity [sin(2x)=2sin(x)cos(x) i.e. sin(x)cos(x)=1/2*sin(2x)] to convert it to 1/4*sin^2(2x) then change that into 1/8*(1-cos(4x)) and proceed to integrate from there. Saves 4 steps.
why do you get - 1/2 cos(4x) when you distribute 1/2 into cos(4x)? wouldn't it be positive 1/2 cos(4x)?
I agree. Antideriv of cos(u) is -sin(u). Nonetheless Patrick is awesome, but I think an error like this should be mentioned
omg are ya a guru,cos ya need to get some creds for dis awesome stuff ya doo,thanks a span man
really good at explaining, thank you
@entrevu
think of it this way, the derivative of sinx is cosx so the anitderivative of cosx is sinx
@patrickJMT there's an easier way of solving this. You could just write the square of sin2x divided by 4 in the beginning instead of using the other formula :)
These videos are great, but I'm a little confused why the final du was 1/4 instead of 4?
I love u man now I understand everything! Keep up the work
bro, at example 1 step 3... u may also simplify 1-cos^2(2x) into sin^2(2x).... the answer will also be the same... just shortcut.. :D
My integration techniques leveled up watching this video!!
thanks chap
I love you so much, thanks a lot you're a life saver!
@RelativisticVeocity ah, i like that!
thank you! this is really helpful.
You saved my life!!
@entrevu no
@entrevu no, dont get confused, the derivative of sinx= -cosx
deeply appreiated
Thanks a lot for giving a better explanation and i hope this topic i can report well to my classmate ^_^
How do you determine which factor you will expand? In the previous video you expanded expanded one factor, in the video above you expand both.
Very helpful. Thank u
this is very great..thenkyuh so much..
now im confused my teacher give me different answer but i think you are right i trust you more than my teacher :D
Thank you
Great info!
when i thought he was done...he kept going!! x_x
Thank you.
why did we get 1/2 x from 1/2 dx??? is there a rule in integrating that says that dx = x while integrating?? doesn't the dx just go away?
Think of dx not just as dx, but as 1*dx. the integral of 1 is x that is where the x is coming from.
If that doesn't help, think of the derivative of x, it is just 1. The integral is just the reverse of a derivative, so the (1/2)*integral(1*dx) must be (1/2)*x
Nick T Aah! thank you!
Integration is kind of inverse of differenciation. Think of it like that
Thank you so much
Great example
integrating trig function would give you more this or add it on your tags i couldn't find your videos by that name. thumbs up so he can see it!!!
Thank u so much prof
Bro!!!! You're my hero!!!!!!
Thanks u so much 4 this, Patrick!
Yesterday in a test i couldnt do it, now i know lol :)
@entrevu you are thinking of the derivative of cos. The Derivative of cos is -sin.
thank you for the video patrick..
but i gotta ask.. in different trigonometric techniques of intergration.
aren't we suppose to use by parts instead of U substitution?
I have a question. In your first problem of this video you have the integral of (sin^2x)(cos^2x) and I get how you did all that, but my book has the same question but instead its the integral of 16(sin^2x)(cos^2x) and they get an answer thats way off and includes cos^3x. Wouldn't you just take out the 16 and distribute it at the end? How does that change the final answer?
you can put number outside of the integral.
at 2:30, it'd be simpler if u replaced the 1-cos^2(2x) with sin^2(2x)
i agree with that to but it isnt right