The average values of a function can be determined by
Use this relationship to verify the results of Eq. (19.13).
To prove: The following results,
If the average value formula is
Explanation of Solution
Given:
The average value formula is
Formula used:
The integral formula are
The trigonometric identity are,
Proof:
Consider the identity,
Use average value formula and take
As it is known that the angular frequency
Therefore,
Use integration formula,
On simplifying further,
Hence, the result is
Now consider next result,
Use average value formula and take
As it is known that the angular frequency
Therefore,
Use the integral formula,
Hence, the result is
Now, consider next result,
Use average value formula and take
As it is known that the angular frequency
Therefore,
Use the trigonometric identity,
Use the integral formula,
Hence, the result is
Now, consider next result,
Use average value formula and take
As it is known that the angular frequency
Therefore,
Use the trigonometric identity,
Use the integral formula,
On further simplifying,
Hence, the result is
Now, consider next result,
Use average value formula and take
As it is known that the angular frequency
Therefore,
Use the trigonometric identity,
On further simplifying,
Hence, the result is
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Chapter 19 Solutions
INTERNATIONAL EDITION---Numerical Methods for Engineers, 7th edition