Consider the region in the first quadrant that is bounded above by the curve
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Consider the region R in the first quadrant that is bounded above by the curve y=x, bounded below by the line y=2x, and bounded on the left by the y–axis.
The region is revolved about the x–axis to generate a solid of revolution.
(a) Determine the x–coordinate of the point where the two bounding curves intersect.
(b) Write, but do not evaluate, the definite integral expression(s) whose value equals the volume of the solid generated by revolving region R about the x–axis.
(c) Evaluate the integral expression(s) from part (b) to obtain the exact volume of the solid.
(d) Indicate whether the integrand(s) you wrote in part (b) represent washer cross-sections or disc cross-sections, and justify your classification.