   Chapter 7.6, Problem 45E

Chapter
Section
Textbook Problem

# (a) Use the table of integrals to evaluate F ( x ) = ∫ f ( x )   d x , where f ( x ) = 1 x 1 − x 2 What is the domain of f and F?(b) Use a CAS to evaluate F ( x ) . What is the domain of the function F that the CAS produces? Is there a discrepancy between this domain and the domain of the function F that you found in part (a)?

To determine

a)To find:

The value of the integral F(x)=f(x)dx where f(x)=1x1x2

Solution:

Domain of F(x) is {x|x(1,0)(0,1]} and the domain of f(x) is {x|x[1,0)(0,1]}

F(x)=ln|1+1x2x|+c

Explanation

The value of the integral F(x)=f(x)dx where f(x)=1x1x2

Formula used:

Entry 35 of integral table duua2u2=1aln|a+a2u2u|+c

Calculation: Given f(x)=1x1x2

f(x)=1x1x2 is defined only if 1x201x1 and denominator is non-zero that is x0, x1 and x1

Hence the domain of f(x)

To determine

b)To find:

Domain using a CAS.

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