   Chapter 12.2, Problem 37E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 39 and 40, (a) evaluate each integral and (b) graph the members of the solution family for C   =   — 5 ,   C   =   0 ,   a n d   C   =   5 . ∫ x ( x 2 − 1 ) 3 d x

(a)

To determine

To calculate: The value of the integral x(x21)3dx.

Explanation

Given Information:

The provided integral is x(x21)3dx

Formula used:

According to the power formula of integrals, if u=u(x), then:

undu=un+1n+1+C

Calculation:

Consider the provided integral:

x(x21)3dx

Rewrite the provided integral by dividing and multiplying by 2 as,

122x(x21)3dx

Consider the power rule of integrals:

undu=un+1n+1+C

Now, to use the power rule, the integrand should have the function u(x) and its derivative u(x) and n1.

Here,

u=x21n=3u=2x

All required parts are present, so the integral is of the form:

122x(x21

(b)

To determine

To graph: The members of the solution family obtained in part (a) for C=5,C=0 and C=5.

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