The region bounded by the parabola and the horizontal line is revolved about the -axis.

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

The region bounded by the parabola

y=x^{2}

and the horizontal line

y=4

is revolved about the

y

-axis. (a) Solve

y=x^{2}

for

x

in terms of

y

on the interval where the rotation occurs. (b) Determine the exact

y

-coordinates of the points where the parabola intersects the line

y=4

and use them to state the limits of integration that will be required to compute the volume of the resulting solid. (c) Compute the exact volume of the solid obtained by this rotation. Show all steps leading to your final answer.

Related theory

Volume Applications
Applications of Integration

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