7 Jan 2022
Problem 49
Page 617
Section 8.7: Taylor and Maclaurin Series
Chapter 8: Infinite Sequences and Series
Textbook ExpertVerified Tutor
7 Jan 2022
Given information
The given integral is 
.
To find the value of the given integral using series to approximate the definite integral.
Step-by-step explanation
Step 1.
Write the binomial Maclaurin series.
Note: use any variable as the second term of the binomial and any other variable to represent the exponent.
Since the radius of convergence 
, then 
. The limits of the integral are within this interval.
, then . The limits of the integral are within this interval.
Substitute into the series:
for 
for 
Then simplify by multiplying the exponents.
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
Solutions
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