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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

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# Homework Help: Please Help Soon thanks

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