Question

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility.

Answer 1

Step 1:

The function is .

Here , and

Trapezoidal Rule:

Let be continuous on . The Trapezoidal Rule for approximating is given by

, where

Using Trapezoidal Rule, .

Answer 2

Contd..

Step 2:

Simpsons rule :

Let be continuous on and let be an even integer,

The Simpsons Rule for approximating is given by

,

where and

Using Simpson Rule, .

Answer 3

Contd..

Step 3:

Graph the function .

Area of the region is 0.55126 sq-units.

Solutions:

Using Trapezoidal Rule, .

Using Simpson Rule, .

Graphically Area of the region is 0.55126 sq-units.