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## Homework Statement

Use the transformation [itex]x= \sqrt{v- u}[/itex], y = u + v to evaluate the double integral of [itex]f(x, y) = \frac{x}{(x^2 + y)}[/itex]

over the smaller region bounded by y = x^2, y = 4 − x^2, x = 1.

## Homework Equations

## The Attempt at a Solution

d:={ (x,y)| [itex]-\sqrt{2}<x<1[/itex] , x^2<y< 4-x^2}

using the jacobian the integral becomes

[tex]\int\int f(x,y)\\da, =\int\int frac{1}{2v}\\dudv[/tex]

[tex]u=\frac{ y-x^2}{2}[/tex]

[tex]v=\frac{y+x^2}{2}[/tex]

but now i am unsure of how to find the limit of integration now

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