The cross-sections are rectangles all of which are 12 m long and have variable width.
To find the width as a function of y --the height above thr ground use similar triangles.
The distance a cross -section is pumped is 7 -y
The int limits are 0 to 4
Don't forget to multiply by g times the densiy of water, which is approximateley 100 Kg/m^3. This gets you the answer in terms of kg-m^2/s^2, or Joules.
Thanks--- I was thinking density =1kg/L which is true but as you pointed out the units would have been off.
1kg/L tranlsates to 1000kg/m^3 not 100
The following attachment reflects the changes-- thanks again