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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 general indefinite integral. Illustrate by graphing several members of the family on the same screen.

( 1 x 2 ) 2 d x

To determine

To find:

The general indefinite integral and illustrate by graphing several members of the family on the same screen.

Explanation

1) Concept:

First, bythe using rules ofthe indefinite integrals, evaluatethe given integral then, by taking several values of C, graph the curves on the same screen.

2) Formula:

i. fx+gxdx=f(x)dx+g(x)dx

ii. xndx=xn+1n+1+C

iii. kdx=kx+C

iv. cf(x)dx=cf(x)dx

3) Given:

1-x22dx

4) Calculation:

As 1-x22=1-2x2+x4

Consider, 1-x22dx= (1-2x2+x4)dx integrating by using the rules of integration,

Separating integral by using the rule,fx+gxdx=f(x)dx+g(x)dx,

1

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