MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Consider the region bounded by the graph of y=x2, the x-axis, and the vertical line x=2. This region is revolved about the horizontal line y=−1 to form a solid S.
(a) Draw and label a representative cross-section that would be used to compute the volume of S by a disc or washer method. Express, but do not evaluate, an integral that represents the volume.
(b) Evaluate the integral from part (a) to obtain the exact volume of S.
(c) Interpret the meaning of your answer in part (b) by stating appropriate cubic units and explaining how the geometry of the region and the location of the axis affect the magnitude of the volume.