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The integral of is easier to evaluate when n is odd.(a)

An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder ISBN: 9780201380279 40

Solution for problem 3P Chapter B

An Introduction to Thermal Physics | 1st Edition

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An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder

An Introduction to Thermal Physics | 1st Edition

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14
1
Problem 3P

The integral of is easier to evaluate when n is odd.

(a) Evaluate(No computation allowed!)

(b) Evaluate the indefinite integral (i.e., the antiderivative) of  using a simple substitution.

(c) Evaluate

(d) Differentiate the previous result to evaluate

Step-by-Step Solution:
Step 1 of 3

ANSWER:

a)

Where the integrand can be written as,

Now the integral will be,

       

This is the integral value.

b)

The same integral can be done by substitution method also.

 

Let ,

Now the integral will be,

         

c)

As,

d)

We know that,

 

         

Step 2 of 3

Chapter B, Problem 3P is Solved
Step 3 of 3

Textbook: An Introduction to Thermal Physics
Edition: 1
Author: Daniel V. Schroeder
ISBN: 9780201380279

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The integral of is easier to evaluate when n is odd.(a)