Region T is enclosed by the curves • • for -values between their two points of…
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Region T is enclosed by the curves
• x=y2
• x=2y+3
for y-values between their two points of intersection. The region T is revolved about the vertical line x=−2 to generate a solid.
(a) Solve for the y-coordinates of the points where x=y2 and x=2y+3 intersect.
(b) Write a piecewise definite integral (with respect to y) whose value equals the volume of the solid formed by revolving T about the line x=−2. Indicate clearly the outer radius, inner radius, and limits of integration on each subinterval.
(c) Evaluate the integral from part (b) to obtain the exact volume of the solid.
(d) Interpret the numerical value obtained in part (c) by stating an appropriate unit of measure and explaining what the value represents in the context of the solid.