(a)

The integral is .

Observe the table :

Here the function is divided into .

There are four mid points,  so consider .

Substitute , and in the above formula.

Midpoint Rule :.

Using the table, substitute corresponding values in the above equation.

.

(b)

for all .

Error in Midpoint Rule :

Suppose for   If  is  error in the Midpoint Rules, then , where is the maximum value of the second derivative in the interval.

Here .

Substitute corresponding values in the above.

Approximate error in the part (a) is .

 (a) .

(b) Approximate error is .