I skipped a lot of steps but here is the Simpon's rule one.
Find the smallest positive integer n so that the maximum error in estimating INTcos(x^3)dx (where b=1 and a=0) by using a) the trapezoid rule, b) simpson's rule is < 1/1000. Then do a) and b) for the max error < 1/100000 on [0, 1] with f(x)=cos(x^3), lf''(x)l<15 and lf^4(x)l<423.
is this problem even in English?? haha. thanks to he/she who helps!