How much work to pump water over edge of trough?

[confused_07]

A 10ft trough filled with water has a semicircular cross section of diameter 4ft. How much work is done in pumping all the water over the edge of the trough? Assume that water weighs 62.5 lb/ft^3.

Confused on how to set up the equation(s). I know:

W= int [a,b] p(h-y) A(y) dy
A= pi*r^2 /2 (since it is a semicircle)
= 6.28

 

[galactus]

Use the equation of a circle: \(\displaystyle \L\\\sqrt{4-x^{2}}\)

The distance each slice is pumped is 2-x.

\(\displaystyle \L\\625\int_{-2}^{0}(2-x)\sqrt{4-x^{2}}dx\)