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Approximate Integral of cos(x^2)

  1. Oct 7, 2012 #1
    1. The problem statement, all variables and given/known data
    I am having issues figuring out the error involved in the trapezoidal and midpoint methods for ∫cos(x^2) from 0 to 1 with n=8


    2. Relevant equations
    |Et|<= k(b-a)^3/(12n^2)
    |Em|<=k(b-a)^3/(24n^2)


    3. The attempt at a solution

    f(x)=cos(x^2)
    f'(x)=-2xsin(x^2)
    f''(x)=-4x^2cos(x^2)

    f''(1) = -3.844

    Is it right given that f''(1) is negative? Just wanted to make sure! Thanks
     
  2. jcsd
  3. Oct 7, 2012 #2

    Ray Vickson

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    Homework Helper

    It doesn't matter: k = max{|f''(x)|: 0 ≤ x ≤ 1}.

    RGV
     
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