Consider the region enclosed by the –axis and the curve for .

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

Problem

Consider the region

S

enclosed by the

y

–axis and the curve

x=y^{2}-4y

for

0\le y\le4

. (a) Determine all values of

y

for which the curve intersects the

y

–axis and label these intersection points on a clearly sketched graph of the region. (b) For each subinterval determined in part (a), indicate whether the curve lies to the left or to the right of the

y

–axis and explain how this affects the integrand when setting up an expression for the area. (c) Set up, without simplifying, a single expression involving definite integrals that represents the exact area of

S

. (d) Evaluate the expression in part (c) to obtain the area of

S

Related theory

Area Between Curves
Area Applications
Applications of Integration

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