❖ Double Integrals - Changing Order of Integration - Full Ex. ❖

Double Integrals - Changing Order of Integration - Full Example.
In this video, I show an example of how to switch the order of integration. I also integrate the function to get the final answer.
In this example we are integrating originally in the form dx dy that we must switch to the form dy dx.
After showing how to switch the order of integration I then proceed to integrate the function.
This example is very important as the original order of integration is very hard to perform but switching makes the integration quite easy.

[@patrickjmt]

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10 years later and you're still saving lives and giving people their engineering degrees. Thanks Pat.

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14 years later 🤩

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glad to help : )

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First of all, thank You! I was revising for my "University math for engineers #4" -course exam (which is, frankly, tomorrow) and got really stuck with these double integrals especially hte changing order of integration. Honestly, I can't even describe how frustratingly I was almost about to give up. But now, all the challenges are overcome and I'm proceeding. Wishing You a happy spring!

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I spent hours pouring over my lecture notes and Calc III book trying to understand this topic without success, but 4 minutes into your video it made complete sense to me. Very well presented--it's incredible to me that my Profs can't explain these topics with 1/10th the clarity. I think your videos are going to become my go-to source for learning new mathematics concepts. Thank you so so much Patrick!

[@skyartineer]

Time it took Patrick to get me to understand this: 8 mins 35 seconds Time it took professor to get me to understand this: I never did to the infinity.

[@timolee8234]

SkyArtineer Try to not think of things in terms of how this is easy and how your professor teaches you something confusing. Remember that the professor is giving the information for a mathematics major- so for us, we need to have all of these other details. Patrick is (excellently) teaching applied mathematics here, not mathematical theory. With an understanding of theory, you should be able to apply it to anything. Its like the difference of being told how to cook a specific recipe, vs. being taught why certain spices go together and methods, and knowing how to cook anything.

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Timo Lee Agreed. I highly doubt some random guy saying he "understands this" after watching this video means that he knows it or even did well when tested on it. It just means you can look at it systematically or easily. However you have to know how to comprehend the entire process to apply it with 100% mastery. Even as a non-math major I understand this pretty easily. It helps a little bit to see all the steps properly but would I say that I now understand this? Nope. It's just in my short-term memory.

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exactly but my professors just focus so much on the theory and forget about how students should apply and eventually gives us very hard exams (and i mean really very hard) that we cant solve ? trust me knowing the theory without knowing how to apply is just useless so i watch professor which actually gives me the theory in a better way and gives examples but takes a long time

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Dude, you are a life saver! I came across this example randomly and was able to use your step by step guide to help me with my Reverse Order problems! Thanks!!!!!!!!!!!!!!!!

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SUBBED!!!!

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i have a calculus exam after 2 hours, your videos allowed me to understand everything i took in the last 3 months. thank you :)

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15years later and you’re still saving my second sem hahaha

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[@tosyn33]

Thanks, I have 2 exams that involve change of integral today, my confidence has been boosted by this video.

[@tosyn33]

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[@StrawberrySong]

You explain this better than my math lecturer at MIT!!

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[@patrickjmt]

Thank you kindly!

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13 years later and you still saved me from failing cal love you man

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15 years later and this is almost the exact problem i have on my homework :)

[@patrickjmt]

@cowzrule101 you just have to look at what is being integrated and think about how you would integrate with respect to x and how you would integrate with respect to y. it may be impossible to do one or the other. i would always draw a graph - but you are basically using inverse functions

[@Escap1st7]

Found this very tricky and complicated to grasp, because my lecturer decided to make it sound as complicated as possible. You simplified everything. Thank you!

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13 years later this is still helpful :) :)

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14 years later and this video is still saving me hahaha! thank you!

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[@patrickjmt]

happy to help :)

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[@patrickjmt]

good luck on the exam!

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That's never coming out to my mind till my tuto and lecturers exposed this idea. Thank u, sir.

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PatrickJMT saving lives out here.

[@kgt94]

Subbed for life, saved me for my final thank you... it makes it so much easier to look at if you make each part of the integration equal to x or y according to the order of integration

[@farbodmirkazemi6378]

It's 2021 and this 8 min video helped me more than a hundred-page book and 2 hours of calculus class.

[@Savvy07]

This is the best and precise explanation to change of order of Integration👍

[@patrickjmt]

well, if the question is: how do i integrate arcsin(x), you use integration by parts.

[@DocHolidayKY99]

Aug 5 2018 - 9:21PM: Calculus 3 final in less than 6 days now and I'm on the verge of failure. I had no idea how to deal with this stuff until now. Thank you professor.

[@patrickjmt]

@AshtonTheGeek no problem. glad you have found them helpful!

[@SunriseAt2008]

Thank you for working out this example completely. It helped me out to understand changing the order of integration as well as calculating the inner integral.

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Better explanation than AI

[@patrickjmt]

lol, damn well better be! :)

[@patrickjmt]

you are very welcome!

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I m here after to watch 12 year old video , which still cleared the concept perfectly for the question that came in my exam... Thankyou

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[@lanomusambazi-tx2eg]

Thank you sir. At least I'm getting some sense from your explanation. I was blank completely. I have never done double integrals before. I'm learning this for the first time. I want to understand more on integrating double integrals before changing the order of integration.

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You were born to teach... Excellent!

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thanks lord patrick i was confused about putting limits from graphs but u made it clear

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Wow I'm in shock right now, I CLEARLY understand the point how can we changing the order of integration! Thank you sooo much man 🙃😊

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The teacher I never had, this made me love maths again

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Saved my day as trying to understand homework. Thanks Patrick kindly.

[@patrickjmt]

glad it helped ya out!

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12 years later and I'm studying engineering and this has helped me , thanks❤❤

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Best explanations ever despite not in my home language👌Things we're expected to know in exams but that are never taught.. Thaaaaaank you so much!

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This example was perfect for me, thanks Patrick.

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Thanks bro, been trying to figure out this concept all night!

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College*

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wow this was the best, i've never understood double integrals so well. thank you!!

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@jesca215 well, i do not do mathematical research, so i am not a mathematician!

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[@jaelbutler7966]

Thanks for this video and the first one. It really helped make sense of how to switch the order of integration and then changing their respective bounds. Thanks, I really appreciated this!

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Patrick, incredibly helpful. So simple when you explain it. Thanks

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it's about to 4am now and it just helped a lot for my exam which is tomorrow:)

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[@patrickjmt]

@stefyburi1 glad you like them : ) just doin' the best i can here...

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Thank you man from Pakistan

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Got this thrown into one of our online open book tests. Our lecturer sped through this semester fairly quickly and entirely missed this. Thanks a lot for the graphical explanation as it helps me a lot when you drew those arrows to understand what reversing actually means. Before watching this vid I kept assuming it meant flipping in y=x

[@mr.kwamid-86_43]

I don't know if it is correct, but what I think you would do is take the limit of the integral as it approaches infinity and see what value it yields.

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Thank you sir my concepts were not clear before this. This is really helpful.

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I hope to pass the exam tomorrow and be an engineer in the future

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