The integral is , .

Consider .

In this case .

Width 

Substitute  and .

.

.

Find the function values.

.

.

.

.

.

Substitute  and  values in .

.

.

.

.

.

Trapezoidal rule:

.

Substitute , , ,  and .

.

Simpsons rule:

.

Substitute , , ,  and .

.

The integral is .

Let 

Apply drivative on each side with respect to .

.

Substitute  and  in .

Substitute .

.

Trapezoidal                Simpsons                        Exact

                                                      .