❖ Calculating a Double Integral ❖
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- Опубліковано 22 жов 2024
- Calculating a Double Integral - Step by Step Examples Explained
Description: Learn how to evaluate a double integral step by step with this clear, detailed example! In this video, I walk through the process of calculating a double integral by hand, focusing on important aspects like integrating with respect to each variable. We will carefully analyze the function of two variables over a specific region, interpreting the integral as the volume bounded between the surface and the xy-plane. This example aims to help students understand the process and avoid common pitfalls in double integral calculations.
What You Will Learn:
How to set up and compute a double integral
Step-by-step process for integrating with respect to both x and y variables
How to interpret the double integral as the volume between a surface and the xy-plane
Tips for avoiding mistakes when calculating double integrals by hand
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#Calculus #DoubleIntegral #Integration #MathTutorial #IntegralExamples #MathHelp #CalculusPractice #PatrickJMT #VolumeCalculations #DefiniteIntegrals #MultivariableCalculus #Calculus3 #MathEducation #IntegralBoundaries #Mathematics #MathVideos #MathExplanation #STEM #MathTeacher
I am a math teacher my self but if I wanna know how to explain things better than what I thought is good then I watch you Patrick. You are the best .
i am very humbled that you feel that way. thanks for the kind words, i appreciate them :)
i would like some more links abt dubble and triple intragation....would u post it?.
Double integral double the difficulty of a single integral, triple integral triple the difficulty of a double integral...
+Fuck Isis
That's a cool name for a math professor
Hey man, that's really nice of you, looking for ways to teach better to your students. That's teacher mvp stuff!
*googles patrickjmt double integrals*
*sees video exists*
Thank God
Patrick is a good tutor!
when you've got your calculus exam tomorrow...
Hahahaa i have calculusexam after 20 hours 😂
+Poker96Face I have after 8 hours!!!
Aravind Raj Good luck bud
+AravindRaj PR me too now
Dana Mateluna finals in 45 minutes
I've been watching your videos ever since I first stepped in college. Some of my profs suck.
I have to say that you have been my math professor for my past three semesters in college. I wish there was a way where I can get the college credits, not pay the school, and instead pay you
IKR. I learn more than I learn from teachers.
Patreon
glad you like my stuff! :) plenty of room for all on the internets though!
Dude you rock. Thank you! I've been out of school for 14 years and forgot how to do this stuff which I suddenly need to know again for my masters degree. You explained this very clearly and succinctly, and it was very easy to follow everything you showed and told me exactly what I needed to know. So thanks for your help!
13 years ago! Will be helpful even more decades
i am gonna try to do this! i plan on making more:
calc 3, linear algebra, differential equations, stats videos this summer.
i also plan on learning physics a bit better (now that i understand the math) after which i will post some of those too!
Wow, I was scared that double integrals would be hard, but its actually really easy!
Same!
Thank you so much for putting in the time to help others out Patrick. I served many years in the Marine Corps and hadn't went over complex math in 8 years. Once my contract ended and I started college again I couldn't completely grasp how my professors were explaining it and after grinding through nearly all of your videos I jumped from Pre-Algebra to Calculus 3 in two quarters through a couple placement exams between a quarter thanks to your video and am about to start my career in Capital Investment. Thanks a ton brother!
yes, i have both. either do a search on my videos, or visit the calculus page of my website
You explain to the core cleanly calmly and to that extent which does not get bored...
Once again, you continue to demonstrate why your style of teaching is superior to the majority of these "professors".
There are good professors. Advantage here is that he makes videos. You can always pause video, hear him well and also you don't have anxiety.
He doesn't actually teach you anything but how to use mathematics as a tool. Now that is definitely great for problem crunching for tests, but this channel isn't a source of understanding. Just because you can now solve the problems in your textbooks doesn't mean you understand them. Don't confuse that.
Actually in university that’s how math looks like for economist and sometimes engenders. In my textbook for “mathematical economics” the literal explanation for why the derivative of a constant is zero was: “The derivative of constant in a function is zero because the Fixed cost never Intersects with the marginal cost. Like c’mon probably Koshi, Newton and all of the crazy ass mathematicians screamed their lungs off when heard that.
Engineers* (sorry for the autocorrect)
Love you Patrick. Thanks for all the help!
Watching exactly 15 years after upload date, nice
Thank you! This is very helpful.
@3:15 you have an iterated integral with f(x,y) := xy + x^2y^3. This is a special case of the form, f(x,y) = g(x)h(y). However, for general f(x,y) "Fubini`s theorem" tells us whether we can integrate `f` as an iterated integral.
i love that last part XD
he was like "I'm lazy so fvck this! this is my final answer!"
it is nice to be in charge
last part is also my fav...😎😎😂
@@patrickjmt HA
anyone else have a midterm in a couple hours? shout out to redbull and patrickjmt!
I really wish I had a math teacher like you when I was in college. This explanation makes understanding double integrals so easy. Patrick - you are just awesome.
glad i could help you out :)
So helpful thanks man
why doesnt our college proffessors teach so well??? i was soo depressed that i wasnt able to understand these stuffs.... god knows wat wud hav happened if youtube wasnt there.... thank u so much sir!!!
This is very clearly described
I had a hard time dealing with my Professor's discussion in Integral Calculus so when I searched some topics in Integral and found out that you had them covered, I was like "finally I can survive this course". So before this semester ends, I would like to thank you for doing math tutorials. It really did help me big time. You're the best Sir! :)
Can't explain to you how much this stuff helps. Was getting stuck in statistics because of these double integrals.
"Back to stuff you saw in first semester calculus..." Honestly, I can't believe there was a time in my life where there would be just simple derivatives and integral problems on an exam. Now learning to work with multivariable functions, vector calculus, even gaining an understand and appreciation of Kepler's laws of planetary motion all in calculus III. It's been a real treat.
it helped me
Thanks, for the variable you treat as a constant i kept making it zero during the integration like with partials derivatives. This video helped me a lot thanks.
@simthadim You're almost right yourself. The integral of 2x is 2x^2/2. The two's cancel and you're left with x^2. The antiderivative formula is X^n+1/n+1. Where n is any whole number.
I don't bother watching the lectures my teachers provide(which arnt even there own content) I am beyond grateful for your videos patrick, short but right to point as always!
I cannot thank you enough!!! It's my 1st time doing double integration but I was not lost at all! You explained it beautifully!!
I'm taking Calc II, in college, and this was the best explanation I have ever experienced for double integrals, thanks!
Dude, it's already 14 years ago. So amazing.
the way i like to think about it is this: you have an equation which gives you a graph, the limits of integration gives you a specific portion of the graph. Now the integral itself allows you to break that portion up into an infinite number of extremely small pieces, and add all infinite number of them together to get an exact value for the area underneath it, did this help?
OMG, i just love allllll your videos. I mean, you have answered one of my questions in the first min and 15 seconds of the video!!!!!Thanks so much!
no problem
Thanks Patrick, your videos have been supremely helpful when my professor's lectures have been utterly useless. Thank you again.
~Ambarenya
Hours wasted on my stupid class notes and textbook dont even come close to this 9min video. THANKYOU SO MUCH PATRICKJMT!!!!!!!!!!
Excellent explanation in its simplicity and context
Beautiful hand writing
thank you SOOOOOOOOOOOOOO much for posting this video. I've spent years not really understanding this concept and after watching this video, I was able to go back and figure it out. THANK YOU SO MUCH!!!!!!
Cheers Patrick, you tought me all of my A - level maths and now you teaching me degree maths :) Its great!!
You know you teach fantastically well when one can understands this without having hardly any background XD.
Wow Nice! I'm taking multivariable calculus this fall and you can say I'm getting a bit ahead of myself, your video's are nice, helps me know what to look forward to this fall and how to do the problems. I've been watching them ever since I had to do sequences and series in calculus II
My last semester of college... Can't remember the last time I did double integrals.
Many many thanks, will be using these videos a lot this semester
You are seriously a God. I have a test tomorrow on this and you are saving my butt. Thank you so much
@YetiSeekingYeti that is not embarrassing at all. i did not take calculus til college myself.
3:04 Linear Algebra!
xD
@soccom8341576
The Lebesgue integral is a generalization of the classical Riemann integral. The class of Lebesgue-integrabelo function is wider than R-integrabele functions. The concept of Lebesgue integral is related to the measure theory and corresponds to the choice of partinioning the y domain, rather than the x domain when one constructs the Riemann sums. To understand Lebesgue integral one has to talk about advanced topics such as Lebesgue measure on the real line, etc...
thanks for the help.
you forgot your brackets when integrating wrt x though.
man im here to thank you, cuz you helped me so much you've been with mee through my calculus I & calculus II, so thank you so much you chenged me really , cheers.
Thanks god for your video. Definitely beats reading long chapters.
36 add 9 is 45 not 44
@Nikon05 ha, glad they help!
im learning this calc 3 over the winter because i want to be the very best there ever was plus i am in competition
Hopefully Patrick not in your competition. Lol
Patrick, you the real M.V.P.
my god, i cant beleive after 6 years i finally understood someone teaching integration,i kind of lost hope and math become my nightmare for life, never cleared a single paper in one attempt.always scrap the last. but if you would have been my math teacher i would have scored a perfect 100, all i needed was patience and a tutor who ll explain all the steps with out skipping.i have exam in a week now i understand the basic.gonna subscribe to your channel :-)
Thanks for sharing your great videos! Your video on calculating a double integral really helped me out in a college class.
Thank you so much Patrick
Awesome explanation! Thank you!
Pre-cal is exactly that, its the math skills you use in a problem before applying calculus.
This means that you use pre-cal in setting up a problem into a form where you can apply calculus. The calculus itself doesn't doesn't involve those skills (essentially).
Business functions don't involve geometry which is a large part of pre-cal math. They are mostly polynomials, radicals, etc. This means to set up a business problem for using calculus you only need algebra 2.
Thank you so much! Clear explanation! This helps me a lot.
You remind me of Paul's Programming ..very easy to follow. Thank you.
This helps a ton. Major props.
A single integral can be used to work out area, a double for volume, a triple for hypervolume, but in our world only single and double are important.
french physics students are thanking you patrick.good job,we learn a lot from you
God knows where I would be if I hadn't found this brilliant youtube channel!
Very informative video! You explained in 8 minutes what my professor couldn't in about 2 hours haha
Thank you!
yes, almost always it is... multivariable calc is usually 3rd semester stuff
thank you patrickJMT you really really
helped me appreciate it.
aww yea! nerdy math guys loves 'internet kisses'! : )
glad it helps!!
There u go the 2nd likes
4 th like was mine
I dont need to attend courses. Just watch you. Professors can't teach as you do. Thanks !
Thank you very much, You've just helped my Uni revision go slightly smoother
I forgot a couple of things and it really helped me remember. Awesome work and please keep it up.
This was incredibly helpful, thank you! Your videos have been saving me this semester. ^.^
thank you!
Thanks brother
dude 1 month of study you made me get it in 8 mins siting in the kichen than you so much .. subscribed
You are the master of masters, the ideal teacher. thanks man
thanks very much keep helping us.
Best youtuber on finals week :D
Excellent teaching .
Thank you very much
You are just born to be the best tutor ever ...
@Pixelize45 Ahhh yes, but you see, his line says "2x..." - so the anti-derivative of that should turn to "2/2*(x^2) ..." which is roughly about the same as "x^2..."
thanks buddy u doing very well. Explanation is soo good and easy to understand
@persinarugabriel00 i know a girl here in the usa that is already through calculus 3 from a top university and she is now gonna be a senior in high school, so i think it depends there, champ
hmm, i faced similar problem when i was doing my A levels... the solution is..simplify it as much as possible and always try to simplify it to the point where you are left with just a number...for example... instead of keeping the answer as (1/3)+(2/3)+3, write it as ANS=4 . if the result doesnt come up as a whole number, dont worry, just try to give the answer as one single fraction (ex. 45/47)..or 0.957(mention the significant figures or decimal places )
Very well-explained. Thank you, sir.
you teach really well.i have an exam tmrw and i finally get it :) THANKYOU
one of the reasons why your videos are so damn good to watch is because of how neat and nice your handwriting is :D
@bearsharrison
pay attention its 45-1-4/3 which equals 44-4/3
Great explanation, thanks man!
thanks alot, you have the best explanations for maths
Professor Patrick! As I know from mathematical rules, at first we have to solve the exercises by this rule : * / + -. I mean at the end of integral it's not correct 9+36 -1 because at first we have to find the solution inside the parenthesis then other part, and at the end the answer would be just 42. :))
that's very useful thank you MR.PATRICK
I wish you were my lecturer!!
Thanks for this!
128 / 3 - Ans .
10years celebration prof!