A region is enclosed by , ,

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A region is enclosed by

y=e^{x}

y=0

x=0

, and

x=1

. The region is revolved about the line

y=4

. A student can set up the volume integral using either

x

y

as the variable of integration. Which of the following best justifies why integrating with respect to

x

is more efficient in this situation? (a) Because the axis of rotation is horizontal, integration with respect to

x

is mandatory. (b) Using

y

would force the shell method instead of washers, which makes the setup much harder. (c) Both the outer and inner radii are easily written directly in terms of

x

, whereas writing them in terms of

y

requires solving

y=e^{x}

for

x

. (d) Since the

y

–bounds would be

0

e

, the irrational upper bound makes the integral more difficult than when using

x

Related theory

Integration Techniques
Volume Applications
Area between curves
Applications of Integration

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