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Fourier Cosine Transforms

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.

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