Use the composite trapezoid rule with 59 subintervals to verify numerically that the approximation obtained agrees with results from Example 3.EXAMPLE 3 If the composite trapezoid rule is to be used to compute01e-x2dxwith an error of at most 1210-4, how many points should be used?Solution The error formula is-b-a12h2f''()In this example, f(x)=e-x2,f'(x)=-2xe-x2, and f''(x)=(4x2-2)e-x2. Thus, |f''(x)|2 on the interval 0,1, and the error in absolute value is no greater than 16h2. To have an error of at most 1210-4, we require16h21210-4,or,h0.01732Since h=1n, we require n58. Hence, 59 or more points are certainly needed to produce the desired accuracy.