Double Integrals - Changing Order of Integration

[rakshakdua]

End is not the end, in fact E.N.D is "Effort Never Dies" & if you get NO in answer, then remember NO is "Next Opportunity". Always be positive...

n now i believe that... i ll pass in 2nd sem :D

[shashank0092]

@rakshakdua gud 1 man :P :D

[Aaroenz0r]

Wow you're amazing, appreciate the good work!

[patrickJMT]

@Aaroenz0r happy to help :) tell your friends!

[RsenOne2]

Thank you.

[MrKunal93]

really thankful to ur videos..... u make maths intresting

[slideyourride90]

3 people don't know what an integral is...

[brady5412]

Thanking you for speaking English!

[tunaisworthnothing]

Isn't this integral equivalent to the single integral x dx from 0 to 1? Is there a point to making it into a double?

[patrickJMT]

@tunaisworthnothing no, it is not the same.

[ImmaculateRecovery]

@patrickJMT

why?

[tadm123]

@tunaisworthnothing when you do double integrals you integrate with respect to x and y. Hence if you only do 0 to 1 the graph would be all shaded from 0 to 1 in x. all from 0 to infinity in y since you don't have boundaries.

[thekendokid]

hey patrick, the graph u drew at the beginning of the video... could that be called "the domain of integration"? Just trying to clarify what that actually means- popped up in a past exam paper.

love your channel btw, its always my first port of call! ;)

[BTNHarmony18]

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[LIGHTSAT1]

the best maths teacher out there

[RowanB86]

Hmm, I think I've worked out why the parameters of the outer integral don't contain x. Is it the case that the parameters I suggested below are valid, but are impractical, as we do not want x in our answer?

[RowanB86]

Would it be wrong if the parameters of the first (inner) integral were 0 to 1, and the parameters of the second (outer) integral were 0 to x?

[RowanB86]

Vert good. Thanks a lot Patrick.

[laurendawe]

Hey Patrick,

How do you know when you need to change the order of integration? Is there a general rule?

[patrickJMT]

@laurendawe well, often times, it may simply be impossible to do it one way or the other; it really just depends on the function you are integrating. so no, i can not see how there would be a general rule

[laurendawe]

@patrickJMT Alright, thanks =) P.s. Love the t-shirt idea!

[duhduhduhduhduh]

Color coded for your convenience.

Do you teach at university? You should. =)

[patrickJMT]

@duhduhduhduhduh i have zero desire to stand at a board and lecture ever again

[rminb010204]

@patrickJMT You should think about teaching highschool Calculus. Students are changing and becoming more academically engaged; good teachers are loved by all students. You never hear the students complain about their grades, or their teachers. My Calculus teacher is probably the favorite among students out of all their teacher.

[patrickJMT]

@rminb010204 i would, except i do not want to deal with: 1) terrible pay 2) red tape/administration junk

3) teaching to an AP/standardized test 4) parents. otherwise i would not mind it at all...

[coralrainsky]

@patrickJMT then what do you do now? with your superior tutoring skills, I think we're all curious as to what a fine young man like you are up to

[MrKyte12]

@patrickJMT ever again? So you teach to o university before.. cool..

[EdgeSteel]

Thank you.

[pablito12sc]

thanks! seriously you kick total ass thanks!!!

[anveshnsk]

fabulous explanation of concept,really very helpful one

[ppppesaaaa]

man..you make it look easy...this is much better than PORN!..thats itt!!!

[nighthawk7948]

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[jDynamicMK]

your method of drawing arrows makes it so easy! i've been studying this topic for hours and i didn't understand it at all until i watched your video for 2 minutes, thanks!

[patrickJMT]

@jDynamicMK magic!

[BazteK7]

@patrickJMT Not just magic... Math Magic!!

[brettrink]

That was fun.

[iWaggD]

you make it so easy, ty

[jaxmwana]

thank you very much... got an exam tomorrow and this has really helped

[xstetsonx]

omg someone who teaches math actually SPEAK ENGLISH!!!!!!!!!!!!!!!!!

[clauclauification]

Thank you for the insight! I was having trouble deciding which region to pick.

[MrBirendrak]

thanks a lot!! it really helped me understand !! I really appreciate your tutorial.....keep posting vids...

[breadandkaya]

omg. thank you so so so so much. this is so helpful

[pawinaz]

thanks so much, that really helped me a lot

[fermixx]

is there a way without graphing and seeing which is the "roof" and "floor" for each variable?

i believe in my exam they are not going to put something so easily graph'able

[spiff33]

fuck shit was so cash. I have a vector calc final in 14 hrs and you are saving my ass right now! Keep the vids comin man, your the best math tutor on youtube.

P.S. Stoke's Theorem would be a nice addition to your videos

[Innapropriate782]

Thanks

[cambassplayer666]

GARRRHHH!! THANKS A LOT!!. you saved me by teaching this b.c it might show up in my calc 3 midterm tomorrow :|! :)

[claudiorebelo]

PS: great vid!

[claudiorebelo]

The way I like to do it is not a formal way but it works. I substitue the double integrals by double sums and substitute what ever function by x(i)y(i). developing the sums a few terms displays the outer integral outside the parenthesis. Applying the simple associative property redifines the new order of integration.

[ravil4]

Thanks for the video!

[calvinhobbesliker2]

This video was very good and informative. However, I would like to know if there's a way to switch the order without having to graph the curves, in case I'd have to graph a 3-d function.

[christopherchubb]

I believe you can just move them as is, what has been done in this video is just making it a bit simpler and placing the unknown limit on the inner integral, but unless there's some reason not to put it on an outer integral I am missing you can just swap as is, as long as the order of your limits still correspond to the order of the dx dy dz or whatever on the end of the equation.

[GrogsLax]

@calvinhobbesliker2 you can probably do it intuitively, but i think there is a higher risk for error