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Math Help - trapezoidal rule

  1. #1
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    trapezoidal rule

    I need to approximate the definite integral using the trapezoidal rule of:
    integral(lower bound 1)(upper bound 5) 1/x^2 * dx; n=4
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    Quote Originally Posted by nystudent2729 View Post
    I need to approximate the definite integral using the trapezoidal rule of:
    integral(lower bound 1)(upper bound 5) 1/x^2 * dx; n=4
    f(x) = \frac{1}{x^2}<br />

    \int_1^5 f(x) \, dx \approx \frac{1}{2}\left[f(1) + 2f(2) + 2f(3) + 2f(4) + f(5)\right] <br />
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  3. #3
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    Trapezoid error estimate

    I need help finding the trapezoid error estimate of: integral(upper bound 5)(lower bound 1) 1/x^2 *dx; n=4
    Thanks.
    I know that the formula is M(b-a)^3/12n^2 but I am having trouble understanding how to find M.
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  4. #4
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    Quote Originally Posted by nystudent2729 View Post
    I need help finding the trapezoid error estimate of: integral(upper bound 5)(lower bound 1) 1/x^2 *dx; n=4
    Thanks.
    I know that the formula is M(b-a)^3/12n^2 but I am having trouble understanding how to find M.
    I assume that this is an upper bound estimate of the error where M is the maximum value of f''(x) over the interval [1, 5] and f(x) = \frac{1}{x^2} ....
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