The curve for x=sqrt(In(y)) for 1<=y<=4 is rotated around the y-axis to form a container. The container is filled with a fluid that weights 80ib/ft^3. Length unites for x and y are in feet.
(a) Set up a definite integral (with respect to y) for the work (in ft-lb) required to empty the container by pumping all of the fluid to the top of the container. (Note: Do not use the acceleration due to gravity; pounds are already a unit of force.)