Let be the region in the first quadrant enclosed by the graphs of and between and

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

Problem

Let

R

be the region in the first quadrant enclosed by the graphs of

y=x

and

y=x^{2}

between

x=0

and

x=2

. When

R

is revolved about the vertical line

x=5

, a solid of revolution is formed. (a) Express each bounding curve as

x

in terms of

y

and state the corresponding interval of

y

over which the expression is valid inside

R

. Give exact values. (b) Write, but do not yet evaluate, a definite integral whose value equals the volume of the solid. (c) Evaluate the integral found in part (b) to obtain an exact value for the volume.

Related theory

Area Between Curves
Area Applications
Volume Applications
Applications of Integration

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