1. Nov 29, 2007

mikejacob33

A river follows the path y = f(z) where x, y are in kilometers. Near the
sea, it widens into a lagoon, then narrows again at its mouth. At the point
(x, y), the depth of the lagoon is given by D(x, y) = 40−160(y−f(x))2 − 40x2 meters. The lagoon itself is described by D(x, y)  0. What is the
volume of the lagoon in cubic meters?

so far i got that this problem needs to use transformation and the jacobian.
i put x=u^2-v^2
y=2uv
find the trans using the matrix getting
4u^2+4v^2
double integral (2uv)(4u^2+4v^2)dudv
if what i did so far was right could anyone tell me how to find the limits or at least enlighten me in the right direction

2. Nov 29, 2007

HallsofIvy

Staff Emeritus
I'm sorry but I have no idea what "D(x, y)  0" means. What that "box" a special symbol?

3. Nov 29, 2007

mikejacob33

sorry i wrote it down wrong
D(x,y)>=0