Consider the region in the –plane bounded above by
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Consider the region in the xy–plane bounded above by y=∣x−1∣, below by the x–axis, and on the left and right by x=0 and x=3, respectively. The region is revolved about the horizontal line y=4 to generate a solid.
(a) Determine the x–coordinate(s) where y=∣x−1∣ intersects the x–axis and explain how these points influence your choice of integration limits.
(b) Write an expression for the volume of the solid as the sum of definite integral(s), clearly stating the outer and inner radii on each sub–interval created by the absolute value function.
(c) Evaluate the integral(s) obtained in part (b) to find the exact volume of the solid.