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    Problem Involving Integration by Parts

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    Please see the attached file for the fully formatted problem involving the cosine function related to integration by parts.

    A_n = l_-1^0 cos n pi t + l_0^1 t cos n pi t dt
    = 1/n pi [sin n pi t]^n_-1 + 1 / n pi [t sing n pi t]^1_0 - 1/npi l_0^1 sin n pi t dt
    = 0 + 0 + 1/(n^2pi^2)[cos n pi t]_0^1
    = { 0 if n is even,
    - 2/(n^2pi^2) if n is odd,

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    Solution Summary

    Integration by parts is explained in this solution. An attached PowerPoint is used to show the answer to the problem.