Region in the first quadrant is bounded on the left by the parabola
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Region R in the first quadrant is bounded on the left by the parabola x=y2, on the right by the line x=2y+1, and below by the x-axis (y=0). Solid S is generated when R is revolved about the y-axis.
(a) Determine the y-coordinates of all points where x=y2 and x=2y+1 intersect.
(b) Using the results from part (a), express the volume of S as a single definite integral with correct limits of integration. Do not evaluate the integral in this part.
(c) Evaluate the integral from part (b) to obtain an exact expression for the volume of S.
(d) State the units of the volume you found in part (c) and briefly explain how those units arise from the problem statement.