Region is enclosed by the curves and for .

MATHEMATICS · Multi-part · A Level · Mathematics · Integration · Integration

Problem

Region

T

is enclosed by the curves

x = y^3 - 3y

and

x = y

for

-2 \le y \le 2

. (a) Determine the

y

-coordinates of all intersection points of the two curves and list the ordered pairs where the curves meet. (b) Set up—but do not evaluate—the definite integral(s) required to compute the area of

T

using vertical slices. (c) Set up a single definite integral that computes the area of

T

using horizontal slices. (d) Evaluate the integral from part (c) to find the exact area of

T

. Then explain why the horizontal-slice method is more efficient for this particular region.

Related theory

Area Applications
Area Between Curves
Applications of Integration

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