# Find the Volume of water in pool using double integrals

## Homework Statement

The depth of water in a swimming pool fits the equation f(x,y) = 2sin (x/20 - 7) - 3 cos ( x-3 /5)+8 when 0<=x<=20 and the sides of the pool fir the equations y(x) = 10-(x-10)^2/10 and y(6)= (x-10)^2/20 -5

Find the volume of the water in the pool using a double integral

I am not sure how to set up this integral. Any help in setting it up will be greatly appreciated.

If you really do want to use a double integral, get that "length" of the rectangle by integrating $\int dy$ with the the parabolic functions as limits.