MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Region W is bounded on the left by the parabola x=y2, on the right by the vertical line x=4, above by the horizontal line y=3, and below by the x–axis. The region is revolved about the vertical line x=6.
(a) Write a definite integral with respect to y that gives the exact volume of the solid formed by revolving W about x=6. Clearly specify the limits of integration and the expressions for both the outer and inner radii.
(b) Evaluate the integral obtained in part (a) to find the exact volume.