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Math Help - Heavily stuck on Newton-Cotes integration

  1. #1
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    Heavily stuck on Newton-Cotes integration

    For an integral of form \int_{-2}^2 x^2e^xdx, calculate the Newton-Cotes quadrature and estimate the error for:

    - n=1 (Trapezoid rule)
    - n=2 (Simpson's rule)
    - n=3 (3/8 rule)
    So I know the formulas for the errors but I don't know what I'm supposed to plug into the formulas... It's very hard to find some examples rather than raw definitions so I'm kind of stuck. Should I solve the initial integral as if it were a regular integral to move on or I'm to plug something into the formula right from the beginning?
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  2. #2
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    Re: Heavily stuck on Newton-Cotes integration

    Hey Glyper.

    What are the formulas for the errors?
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  3. #3
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    Re: Heavily stuck on Newton-Cotes integration

    -\frac{(b-a)^3}{12}\,f^{(2)}(\xi) for trapezoid rule, -\frac{(b-a)^5}{2880}\,f^{(4)}(\xi) for Simpson's rule and -\frac{(b-a)^5}{6480}\,f^{(4)}(\xi) for 3/8 rule.
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