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I have posted a link there to this topic so the OP can see my work.Calculus Integration Problem?

y = tan−1 x between x = 0 and x = 1 is rotated around the y axis to form a container. The container is filled with water. Use n = 6 subintervals and Simpson's rule to approximate the work required to pump all of the water out over the side of the container. Give your answer in decimal form.

(Distance is measured in meters, the density of water is 1000 kg/m3, and use 9.8 m/s2 for g.)

I know that I should use cylindrical shells as it is rotated by the y-axis. But beyond that I' am having trouble setting up the integral and evaluating it with Simpson's.

Thanks for the help in advance!