A region is bounded on the left by the curve and on the right by the curve
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A region S is bounded on the left by the curve x=y2 and on the right by the curve x=4y−y2. The region is revolved about the vertical line x=6, generating a solid.
(a) Determine all y-values where the curves x=y2 and x=4y−y2 intersect. Show all algebraic steps.
(b) For every y in the interval found in part (a), identify which of the two curves is farther from the line x=6. Provide analytic justification for your choice.
(c) Construct a single definite integral that represents the volume of the solid, clearly indicating the limits of integration and the integrand.
(d) Evaluate the integral in part (c) and give the exact volume.