The function is .

(a) Trapezoidal Rule:

Let  be continuous on .

The Trapezoidal Rule for approximating  is given by

, where  \ \

Here ,  and .

Width of the interval  .

End points are and .

Using trapezoidal Rule, .

(b) Midpoint Rule:

Let  be continuous on .

The Midpoint Rule for approximating  is given by

, where 

Width of the interval  .

Midpoints are . 

Using Midpoint Rule, .

(c) Simpsons rule :

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

where  .

Determine by simpsons rule:

and Width of the interval  .

Using Simpson Rule, .

(a) Using trapezoidal Rule, .

(b) Using Midpoint Rule, .

(c) Using Simpson Rule, .