Question

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.)

Answer 1

Step 1:

(a)

The function is .

Here , and .

Trapezoidal Rule:

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

, where

Using Trapezoidal Rule, .

Solution:

(a) Using Trapezoidal Rule, .

Answer 2

Step 1:

(b)

The function is .

Here , and .

Midpoint Rule:

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

, where

Using Midpoint Rule, .

Solution:

(b) Using Midpoint Rule, .

Answer 3

Step 1:

(c)

The function is .

Here , and .

Simpson's Rule:

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

,

where and

Using Simpson Rule, .

Solution:

(c) Using Simpson Rule, .