(a)

The integral is .

Observe the table :

There are intervals in the function.

Substitute , and in the above formula.

Simpsons Rule :.

.

(b)

for .

Error Bound for Simpsons Rule :

Suppose for . If  is  error in the Simpsons Rules, then .

is the maximum value of the second derivative in the interval.

Here .

Substitute corresponding values in .

Approximate error in the part (a) is .

 (a). .

(b). Approximate error is .