Ashley P.

asked • 05/09/23

Change of Variables - Double Integrals

Could someone let me know how we could solve this question related to change of variables in double integrals?


I've also included my work in: drive(DOT)google(DOT)com/file/d/1-QwMt5PTChRreTDPmeWdRx2CQ48pWpCl/view?usp=drivesdk

Roger R.

tutor
Since the integrand is never negative, the integral will have a positive value. The transformation T(r,θ) maps your domain D' = [0,1]×[0,2π] onto a full circle, not the triangle (0,0)(1,0)(1,1) defining the domain D of the integral.
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05/09/23

Ashley P.

So, have I done this correctly?
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05/09/23

Roger R.

tutor
No, you haven't. You have to pay more attention to the two domains linked by the transformation T (change of variables). T must be a bijection (except for a null set that would not matter when integrating).
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05/09/23

Roger R.

tutor
Instead of switching directly to polar coordinates, consider first doing a change in the order of integration (Fubini): ∬{...}dydx = ∬{...}dxdy. You must again carefully check the x- and y-intervals for the two integrals.
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05/09/23

Ashley P.

Sorry, but I still don't see the way ahead
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05/09/23

1 Expert Answer

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Melanka W. answered • 05/09/23

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