(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let I=∫∫_{D}(x^{2}−y^{2})dxdy, where

D=(x,y): {1≤xy≤2, 0≤x−y≤6, x≥0, y≥0}

Show that the mapping u=xy, v=x−y maps D to the rectangle R=[1,2]χ[0,6].

(a) Compute [itex]\frac{\partial(x,y)}{\partial(u,v)}[/itex] by first computing [itex]\frac{\partial(u,v)}{\partial(x,y)}[/itex].

(b) Use the Change of Variables Formula to show that I is equal to the integral of f(u,v)=v over R and evaluate.

2. Relevant equations

3. The attempt at a solution

(a) [itex]\frac{\partial(u,v)}{\partial(x,y)}[/itex]=|-(y+x)|

so, [itex]\frac{\partial(x,y)}{\partial(u,v)}[/itex]=[itex]\frac{1}{y+x}[/itex]

(b)I have to evaluate I, but I have no idea how, please help!!

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# Homework Help: Help with Change of variables and evaluating area?

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