Approximate the following integrals with rectangular and simpson's rule

Question

in both cases use 10 subintervals.

Answer 1

(1)

Evaluate using Rectangular Method.

Step 1:

The function is .

Here , and .

Number of subintervals .

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 :

.

Answer 2

(1)

Evaluate using Simpson's Method.

Step 1:

The function is .

Here , and .

Number of subintervals .

Simpson's 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:

.

Answer 3

2)

Evaluate using Rectangular Method.

Here , and .

Rectangular method is also known as Midpoint method.

Midpoint Rule:

Let be continuous on , the Midpoint Rule for approximating is given by

, where  and

.

Using Midpoint Rule, .

Solution:

.

Answer 4

2)

Evaluate using Simpson's Method.

Here , and .

Number of subintervals .

Simpson's 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:

.