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Fourier Cosine Transforms

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Please see attached file. Please show all steps in detail.

In the two problems below find the Fourier Cosine Transform of the given f(x) and write f(x) as a Fourier integral.

1)
-1, -Pi <x<0
f(x) = 1, 0<x<Pi
0, |x| > Pi

2)
2x+2a -a<x<0
f(x) = -2x+2a 0<x<a
0 |x|>a

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Solution Summary

Fourier cosine transforms are investigated. The functions are solved.

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Exponential Fourier Transforms and Fourier Integrals

Please see the attached file for the fully formatted problems.

In the two problems below find the exponential Fourier Transform of the given f(x) and write f(x) as a Fourier integral.

2)
2x+2a -a<x<0
f(x) = -2x+2a 0<x<a
0 |x|>a

The Fourier is of the type
(see attachment).

Please do this problem manually (without tables) and please show all work including integrations.

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