(1)

Step 1:

The function is .

Here , and .

Number of sub intervals .

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, .

Solution:

.

(1)-(b)

Step 1:

The function is .

Here , and .

Number of sub intervals .

Rectangular method is also known as Midpoint method.

Midpoint Rule:

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

, where

Using Midpoint Rule, .

Solution :

.