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Use the results (5.105) and (5.106) to prove the formulas

Chapter 5, Problem 5.48

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QUESTION:

Use the results (5.105) and (5.106) to prove the formulas (5.83)(5.85) for the Fourier coeffi-cients an and bn. [Hint: Multiply both sides of the Fourier expansion (5.82) by cos(mwt) or sin(mwt) and then integrate from z/2 to r/2.]

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QUESTION:

Use the results (5.105) and (5.106) to prove the formulas (5.83)(5.85) for the Fourier coeffi-cients an and bn. [Hint: Multiply both sides of the Fourier expansion (5.82) by cos(mwt) or sin(mwt) and then integrate from z/2 to r/2.]

ANSWER:

Step 1 of 3

The Fourier series is

                  

Multiply the above equation with  and integrate within the limit with respect to

But,

                                      

Thus all the terms containing the coefficients  and  will become zero except for  

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