hey everyone

The question i got was that estimate the minimum number of subintervals with an error of magnitude less than 10^-4 by the trapezoidal rule and the simpson rule for the integral( x^3 + x) from 0 to 2

i did the trapezoidal rule

10^-4 = 6t(2-0)^3 / (12n^2)

f''x is greatest at t=2

n = 282.84 which if approximated is 283

so n = 283

for Simpson rule i did:

10^-4 = 0(2-0)^5 / (180n^4)

but i get n = 0 which i think either isn't right or the simpson rule does not have an error.

can someone tell me if i did it right and also that whenever i get f''x or f''''x, do i always have to get a t between [a,b] that gives me the greatest value for f''x or f''''x

thanks alot