- #1

- 2

- 0

**Calculus: Coordinate Changes, Jacobian, Double Integrals??**

## Homework Statement

Show that T(u,v) = (u

^{2}- v

^{2}, 2uv)

maps to the triangle = { (u,v) | 0 ≤ v ≤ u ≤ 3 } to the domain D,

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

^{2}= 324 - 36x.

Use T to calculate ∬sqrt(x

^{2}+y

^{2}) dxdy on the region D.

## Homework Equations

## The Attempt at a Solution

I know that dxdy = the Jacobian = (4u

^{2}+4v

^{2})dudv.

I'm have a really hard time finding a way to figure what the bounds of the integral are, in terms of u and v.