Problem 4E

If the Midpoint Rule is used on the interval [−1, 11 j with n = 3 subintervals, at what x- coordinates is the integrand evaluated?

Solution:-

Step1

Given that

If the Midpoint Rule is used on the interval [−1, 11 ] with n = 3 subintervals.

Step2

To find

At what x- coordinates is the integrand evaluated?

Step3

Midpoint rule

Hence the 3 subintervals are [-1,3],[3,7],[7,11]

Step4

Midpoints of these intervals are given by

So,

Hence the x- coordinates at which the integrand is evaluated in midpoint rule are 1,5,9.