The Errors in the Trapezoid Rule and Simpson's Rule

If f"(x) is continuous in [a, b], then the error in the trapezoid rule is no larger than

    (b - a)3

    12n2
    |f"(M)|,

where |f"(M)| is the largest value of |f" (x)| in [a, b].


If f(4)(x) is continuous in [a, b], then the error in Simpson's rule is no larger than

    (b - a)5

    180n4
    |f(4)(M)|,

where |f(4)(M)| is the largest value of |f(4)(x)| in [a, b].


Just close this window to return to the exercises.