A solid occupies the segment on the x-axis

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A solid occupies the segment −1≤x≤5-1\le x\le 5 on the x-axis. • For −1≤x≤1-1\le x\le 1, the cross sections perpendicular to the x-axis are squares with side length 22 units. • For 1≤x≤31\le x\le 3, the cross sections are rectangles whose height is 33 units and whose width is xx units. • For 3≤x≤53\le x\le 5, the cross sections are squares with side length 5−x5-x units. Determine the exact volume of the solid.

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