- #1
mikejacob33
- 2
- 0
Please Help Soon!thanks
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
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