A trough has a trapezoidal cross section with a height of 5 m and horizontal sides of width 5/2 m and 5 m. Assume the length of the trough is 10 m. Complete parts? (a) and? (b) below.

a) How much work is required to pump the water out of the trough? (to the level of the top of the? trough) when it is? full? Use 1000 kg/m3 for the density of water and9.8 m/s2 for the acceleration due to gravity. Draw a? y-axis in the vertical direction? (parallel to? gravity) and use the midpoint of the bottom of one edge of the trough as the location of the origin. For 0?y?5?, find the? cross-sectional area? A(y) in terms of y.

b) Set Up the integral that gives the work required to pump the water out of the tank.