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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find (approximately) the area of the region bounded by the curves.

y = 3 x 2 2 x ,   y = x 3 3 x + 4

To determine

To find:

Approximate x-coordinates of the points of intersection of the given curves, and find the area of the region bounded by the curves.

Explanation

1) Concept:

Formula:

The area A of the region bounded by the curves y=f(x), y=g(x) and the lines x=a and x=b is

A= abfx-gxdx

fx-gx=fx-gx when fxg(x)gx-fx when gxf(x)

2) Given:

y=3x2-2x,   y=x3-3x+4

3) Calculation:

fx=3x2-2x and gx=x3-3x+4

i) To find the intersection point of the curves, draw the graph.

From the sketch, it is clear that the curves intersect at x-1.11, x1.25 and x2.86

in the interval [-1.11, 1.25] the upper curve is y=x3-3x+4  and the lower curve is y=3x2-2x

and in the interval 1.25, 2.86, the upper curve is y= 3x2-2x and the lower curve is y=x3-3x+4

Therefore,

A=-1

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