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Math Help - Function approximation

  1. #1
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    Function approximation

    Use the first three terms of the series expansion as an approximation for the function to be integrated. Estimate the value of the definite integral.
    \int^{0.2}_{0.1} \sqrt[3]{1-x^2} dx
    series expansion:
    (1-x^2)^{\frac{1}{3}}=1-\frac{1}{3}x^2-\frac{1}{9}x^4
    so i have:
    \int^{0.2}_{0.1}(1-\frac{1}{3}x^2-\frac{1}{9}x^4) dx
    =[x-\frac{1}{9}x^3-\frac{1}{45}x^5]^{0.2}_{0.1}
    =0.09921533
    answer is 0.9921556
    Where is my error?
    Thanks
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  2. #2
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    Quote Originally Posted by arze View Post
    Use the first three terms of the series expansion as an approximation for the function to be integrated. Estimate the value of the definite integral.
    \int^{0.2}_{0.1} \sqrt[3]{1-x^2} dx
    series expansion:
    (1-x^2)^{\frac{1}{3}}=1-\frac{1}{3}x^2-\frac{1}{9}x^4
    so i have:
    \int^{0.2}_{0.1}(1-\frac{1}{3}x^2-\frac{1}{9}x^4) dx
    =[x-\frac{1}{9}x^3-\frac{1}{45}x^5]^{0.2}_{0.1}
    =0.09921533
    answer is 0.9921556
    Where is my error?
    Thanks
    I don't see an error here.
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  3. #3
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    ok, then the other explanation is the answer is inaccurate?
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