A region is enclosed by the curve

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Integrals · Applications of Integrals

Problem

y=\sqrt{x}

, the horizontal line

y=2

, and the

y

-axis (

x=0

). The region is revolved about the

x

-axis, producing a solid with a hollow center. (a) Determine the limits of integration and the expressions for the outer and inner radii required to compute the volume of the solid. (b) Set up and evaluate the definite integral that gives the exact volume of the solid. Express your answer in terms of

\pi

Related theory

Volume Applications
Applications of Integration
Area under a curve
Area under simple curves

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