Region is enclosed by the graphs of and on the interval
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Region U is enclosed by the graphs of y=sinx and y=cosx on the interval 0≤x≤4π. The region is revolved about the horizontal line y=−1, producing a solid.
(a) On the interval 0≤x≤4π, determine which of the two functions is farther from the line y=−1. Justify your answer analytically.
(b) Using your result from part (a), write a definite integral that represents the volume of the solid.
(c) Evaluate the integral from part (b) to obtain an exact expression for the volume of the solid. Show all steps of your calculation.