Mathematics

Mathematics

Problem

A solid has base the disk x2+y2≤9x^{2}+y^{2}\le 9 in the xyxy-plane. For each xx in the interval −3≤x≤3-3\le x\le 3, the cross section perpendicular to the xx-axis is a rectangle whose width equals the full vertical length of the base at that xx and whose height is 5−x25-x^{2}. Determine the volume of the solid.

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