Region S is bounded by , ,

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

Problem

Region S is bounded by

y=e^{x}

y=0

x=0

, and

x=1

. Without performing any detailed computations, which choice correctly identifies the variable of integration that minimizes algebraic complexity and gives the best justification? (a) Integrate with respect to

y

, because the limits of integration are simply

0

e

, so no splitting is required. (b) Integrate with respect to

y

, because

\ln y

is simpler to integrate than

e^{x}

. (c) Integrate with respect to

x

, because two separate integrals would be required if

y

were the variable. (d) Integrate with respect to

y

, because the integrand becomes linear once the curves are written as functions of

y

Related theory

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

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