anonymous
  • anonymous
Calculus II- Double Integral [see attachment]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
anonymous
  • anonymous
simple, first do this integration \[\int\limits_{}^{} y dy\]
anonymous
  • anonymous
It's supposed to integrated first with respect to x and then with respect to y. But there is no x value.

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anonymous
  • anonymous
? you do the inner integral first which is respect to y
anonymous
  • anonymous
unless the problem is asking you to change the order in which you integrate then you need to draw the picture out and redefine the bounds
anonymous
  • anonymous
are there any other instructions other than evaluate the integral?
anonymous
  • anonymous
no... just find the double integral... so the inner integral is y^2/ 2 right?
anonymous
  • anonymous
yes and its from 2x to x^2
anonymous
  • anonymous
so you substitute those in
anonymous
  • anonymous
but those are for x values I thought. so it wouldn't go into y?
anonymous
  • anonymous
and 5 to 1 would go into y^2/2
anonymous
  • anonymous
the integral to put it in another way \[\int\limits_{y= -2x}^{y=x^2}y dy\]
anonymous
  • anonymous
\[(x^2)^2/2 - (-2x)^2/2\]
anonymous
  • anonymous
you cant change the order ex. \[\int\limits_{a}^{b} \int\limits_{c}^{d} xy dx dy = \int\limits_{c}^{d} \int\limits_{a}^{b} xy dy dx\]
anonymous
  • anonymous
but you cant just switch the cd and ab around without switching the dy and dx
anonymous
  • anonymous
ok anyways assuming you're right \[\int\limits_{0}^{2} \frac{ (x^2)^2}{2} - \frac{ (-2x)^2}{2} dx\]
anonymous
  • anonymous
then you take the outer integral
anonymous
  • anonymous
... now I'm lost.
anonymous
  • anonymous
@Loser66 his problem was he was trying to take the integral of \[\int\limits_{-2x}^{x^2}\int\limits_{0}^{2}y dy dx\]
anonymous
  • anonymous
So with my equation I gave you I subtracted them \[\frac{ x^4 }{ 2 } - 2x^2\]
anonymous
  • anonymous
k, then you do the other integral
anonymous
  • anonymous
so the integral \[\int\limits_{0}^{2} \frac{x^4}{2} -2 x^2 dx\]
anonymous
  • anonymous
outer not other...
anonymous
  • anonymous
I get... 0?
anonymous
  • anonymous
really?
anonymous
  • anonymous
|dw:1370654147308:dw|
anonymous
  • anonymous
thank you future
anonymous
  • anonymous
Any time :)
anonymous
  • anonymous
Medal? xD
anonymous
  • anonymous
thank you.
anonymous
  • anonymous
i suggest you double check your work @MCJones9879 and see where you made the mistake you have the solution to work off of so it shouldnt be hard
anonymous
  • anonymous
Although I prefer polar coordinate shaha
anonymous
  • anonymous
they're not that different

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