Let on . The region under the graph of on this interval is the base of a solid with…
MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Let f(x)=3−x on 0≤x≤3. The region under the graph of f on this interval is the base of a solid with cross sections perpendicular to the x-axis described below:
• For 0≤x≤1.5, each cross section is an isosceles right triangle with legs of length f(x).
• For 1.5<x≤3, each cross section is a semicircle whose diameter is f(x).
Compute the exact volume of the solid.