Science:Math Exam Resources/Courses/MATH307/December 2010/Question 06 (f)/Solution 1

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If we extend the domain from to , we can write the new Fourier coefficients using the techniques from part (a) as

We could go and directly compute these integrals but we want to relate them to the coefficients from part (a) computed on a domain . To do this, we can use a substitution and let . Then . With this transformation we have and and so putting everything together,

where we have recognized that the new integral is precisely what we computed to get the coefficients on a period . Therefore on the Fourier coefficients double and

Therefore we have that and the points to plot for the frequency amplitude are .