- #1

Suy

- 101

- 0

## Homework Statement

Show that T(u,v) = (u

^{2}- v

^{2}, 2uv)

maps to the triangle = {(u,v): 0 ≤ v ≤ u ≤ 4} to the domain D

bounded by x=0, y=0, and y

^{2}= 1024 - 64x.

Use T to evaluate ∬

_{D}sqrt(x

^{2}+y

^{2}) dxdy

## Homework Equations

## The Attempt at a Solution

x=u

^{2}-v

^{2}

y=2uv

Jacobian= 4u

^{2}+4v

^{2}dudv

I guess the equation in the changed variable integral should be ∫∫sqrt((u

^{2}-v

^{2})

^{2}+(2uv)

^{2}) (4u

^{2}+4v

^{2}) dudv

But, I don't know how to get the bounds for the integrals in terms of u and v.

Can someone help me on this??