Question

Evaluate by using Rectangular and trapezoidal rule with 10 sub intervals.

Answer 1

(3)

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 and  .

.

Using Midpoint Rule, .

Solution :

.

Answer 2

(3)

Evaluate using Trapezoidal Rule.

Step 1:

The function is .

Here , and .

Number of subintervals : .

Trapezoidal Rule:

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

,

where and  .

.

Using Trapezoidal Rule, .

Solution :

.

Answer 3

(4)

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 and  .

.

Using Midpoint Rule, .

Solution :

.

Answer 4

(4)

Evaluate using Trapezoidal Rule.

Step 1:

The function is .

Here , and .

Number of subintervals : .

Trapezoidal Rule:

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

,

where and  .

.

Using Trapezoidal Rule, .

Solution :

.

Answer 5

(5)

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 and  .

.

Using Midpoint Rule, .

Solution :

.

Answer 6

(5)

Evaluate using Trapezoidal Rule.

Step 1:

The function is .

Here , and .

Number of subintervals : .

Trapezoidal Rule:

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

,

where and  .

.

Using Trapezoidal Rule, .

Solution :

.