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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

Find the area of the region bounded by the given curves.

x + y = 0 ,    x = y 2 + 3 y

To determine

To find:

The area of region bounded by given curves.

Explanation

1) Concept:

The area A of the region bounded by the curves x=fy& x=gy, and the lines y=c, y=d, where f and g are continuous and fyg(y) for cyd, then area is

A= cdfy-gydy

2)  Given:

The region bounded by the curves x+y=0 and   x=y2+3y

3) Calculation:

As the given region is bounded by the curves x+y=0 and x=y2+3y,

From the graph, the right boundary curve is x+y=0 x=-y and the left boundary curve is

x=y2+3y

x=-y and x=y2+3y intersect each other when, -y=y2+3y

y2+4y=0,  yy+4=0

  y=0 or y=-4

Therefore, the area of the region bounded by the curves x=-y and x=y2+3y between x=-4 to x=0 is given by

A= 

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