ok, somebody please tell me where I am going wrong.

Basically, I am integrating along the side with length C, so my largest recangle would be 6 times 9 (or a times b). I place the x-axis along side with length c of the triangle that's facing us. so each of the layer i am working with is vertical. This should work, becuase if you basically rotate the image, you can still visualize the water as being pumped towards the faucet right?

i used similar triangles, so using the triangle that faces us, we get (y/(13-x) = 6/13. thus 13y = 78-6x so y = 6-(6x/13).

volume of each prism would equal (6-(6x/13)) * 9 * delta x.

Force = 62.5 * 9 * (6-(6x/13)) * deltax

work = 562.5 * (6-(6x/13)) * x deltax

i integrated the work function from 0 to 13, and i get 95062.5 but the my online homework checker says its wrong. it doesnt tell me the correct answer, but can somebbody please tell me where I am going wrong?