Midpoint Rule approximations

Find the indicated Midpoint Rule approximations to the following integrals.

using n = 1, 2, and 4 subintervals

Problem 12E

Midpoint Rule approximations Find the indicated Midpoint Rule approximations to the following integrals. using subintervals.

Step 1</p>

In this problem we have to find the midpoint rule approximation to using subintervals.

First let us see about midpoint rule approximation.

The midpoint sum (or midpoint rule approximation) using midpoints of subintervals n is given by

…. (1)

where

Step 2</p>

Now let us find the midpoint rule approximation to with

We have and

Therefore

Hence Divide into subintervals of length with the following end points

Now we just evaluate the function at those points.

Thus by using (1) the midpoint approximation of with n=1 is given by

Thus the midpoint approximation of with n=1 is 1000.