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Math Help - definite integral, w/ power series.

  1. #1
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    definite integral, w/ power series.

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

    INT 0_0.2 1/(1 + x^5) dx

    its definite from 0 to 0.2 showed above there.

    appreciate any help for this one. integrals are difficult for me with series especially.

    thankyou.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by rcmango View Post
    have to Use power series to approximate the definite integral to six decimal places.

    INT 0_0.2 1/(1 + x^5) dx

    its definite from 0 to 0.2 showed above there.

    appreciate any help for this one. integrals are difficult for me with series especially.

    thankyou.
    1/(1+x^5) = 1 - x^5 + x^10 - R(x)

    with remainder R(x)>0, less than 0.2^15 on (0, 0.2)

    Therefore:

    I = INT 0_0.2 1/(1 + x^5) dx = integral_{x=0 to 0.2} 1 - x^5 + x^10 - R(x) dx

    ..................................= 0.2 - (0.2)^6/6 + (0.2)^11/11 + epsilon

    where |epsilon| < (0.2)^16.

    So I ~= 0.194444 to six decimal places

    RonL
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  3. #3
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    thankyou.
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