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Math Help - approximate integral using power series

  1. #1
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    approximate integral using power series

    0 int 0.2

    1/(1+x^5) dx

    need to use power series to approximate the definate integral.

    thankyou for help on this one!
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  2. #2
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    Quote Originally Posted by rcmango View Post
    0 int 0.2

    1/(1+x^5) dx

    need to use power series to approximate the definate integral.

    thankyou for help on this one!
    From the geometric power series

    \frac{1}{1+x} = 1 - x + x^2 - x^3 + - \cdots

    \frac{1}{1+x^5} = 1 - x^5 + x^{10} - x^{15} + - \cdots

    so

    \int_0^{0.2}\frac{1}{1+x^5}\, dx = \int_0^{0.2} 1 - x^5 + x^{10} - x^{15} + - \cdots \, dx

    and integrate term-by-term (you won't need a lot of terms to get a really accurate answer)
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