TylerD
  • TylerD
double integral
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
TylerD
  • TylerD
\[\int\limits_{0}^{\sqrt{\Pi}}\int\limits_{x}^{\sqrt{\Pi}}2\cos(y^2)dydx\]
TylerD
  • TylerD
evaluate by reversing order it says
ganeshie8
  • ganeshie8
As a start, sketch the region of integration

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TylerD
  • TylerD
i did
ganeshie8
  • ganeshie8
take a screenshot and post if psble
TylerD
  • TylerD
|dw:1447162041164:dw|
ganeshie8
  • ganeshie8
|dw:1447162146410:dw|
ganeshie8
  • ganeshie8
changing the order to `dxdy` means that you want to fix `y` first and see how function changes as `x` is increased
ganeshie8
  • ganeshie8
fix `y` value, shoot a horizontal arrow through the region : |dw:1447162334126:dw|
ganeshie8
  • ganeshie8
Look at that arrow, whats the x where when it enters the region ? whats the x value when it leaves the region ?
ganeshie8
  • ganeshie8
|dw:1447162455685:dw|
ganeshie8
  • ganeshie8
therefore the new bounds would be : \(y:0\to \sqrt{\pi}\) \(x : 0\to y\)
ganeshie8
  • ganeshie8
the integral becomes \[\large \int\limits_{0}^{\sqrt{\Pi}}\int\limits_{0}^y 2\cos(y^2)dxdy\]
TylerD
  • TylerD
dont even know how id eval cos(y^2) lol
mathmate
  • mathmate
hint: it's easier to integrate ycos(y^2) than cos(y^2) alone.

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