A region in the first quadrant is bounded above by the line
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A region R in the first quadrant is bounded above by the line y=2x, below by the parabola y=x2, and on the left by the y-axis. The region is revolved about the y-axis, producing a solid.
(a) Determine the x-coordinates of the points where y=2x and y=x2 intersect.
(b) For each y in the interval determined in part (a), express the x-coordinates of the bounding curves as functions of y.
(c) Identify which curve generates the outer surface of the solid and which generates the inner surface, and explain your reasoning in terms of distance from the axis of rotation.
(d) Write, but do not evaluate, a definite integral that represents the volume of the solid.