A tank is in the shape of the curve y = 8(x^3)for 0 x 1 revolved about the y axis, withthe x and y axes labeled in feet. Suppose the tank is filled...

A tank is in the shape of the curve y = 8(x^3)for 0 ≤ x ≤ 1 revolved about the y axis, withthe x and y axes labeled in feet. Suppose the tank is filled with water weighing 62.5 lbs/ft3. Draw a picture of the situation. Then write down the integral for the work W required to bringthe water to the top of the tank until there is a depth of 1 foot of water in the tank. Preparethe integral for integration, but DO NOT EVALUATE THE INTEGRAL