Find work to empty trough by pumping the water over the top of it?

A trough is 8 ft lng and 1 ft high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y = x^10 from x = -1. The trough is full of water. Find the amount of work in ft-lbs required to empty the trough by pumping the water over the top.





The wt. of water is 62 lbs/ft^3

Find work to empty trough by pumping the water over the top of it?
I have oriented the trough in the following way,the bottom edge is kept on the z axis(along the positive z direction),with the two tripod faces being parallel to the xy plane and the top rectangle is parallel to xz plane.





Elementary work done in lifting a small portion of water of width dy is


dW=mass * g * height





mass of water = density (ρ)X Volume


Volume of water as a function y (y being taken from y=0 to y=1) is 2*y^(1/10)dy*8(This can be easily derived through a simple double integral)


so,


W=16* ρ*g∫(1-y)*y^(1/10)dy,from 1 to 0


Solve this integral to get the answer





Hope I'am Correct!