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Math Help - Power series to find an integral

  1. #1
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    Power series to find an integral

    Hello, I'm having trouble with the question below. I'm supposed to use a power series to approximate this integral, but the way I tried it seemed to fail horribly. Does anybody know how to do this?

    Use a power series to approximate the definite integral to six decimal places.


    What I tried was to take the derivative, then make a power series for that, and then integrate that summation twice. That's most likely wrong, but I'm not sure why. Any help would be appreciated.

    Thank you
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by bnay View Post
    Hello, I'm having trouble with the question below. I'm supposed to use a power series to approximate this integral, but the way I tried it seemed to fail horribly. Does anybody know how to do this?

    Use a power series to approximate the definite integral to six decimal places.


    What I tried was to take the derivative, then make a power series for that, and then integrate that summation twice. That's most likely wrong, but I'm not sure why. Any help would be appreciated.

    Thank you
    Note that \ln (1 + x) = \sum_{n = 1}^\infty (-1)^{n+ 1}\frac {x^n}n for |x| \le 1, x \ne -1

    now replace x with x^5 everywhere, then integrate term by term
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