Question

Use Simpson’s Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator.

y = x sin x,        0 ≤ x ≤ 2π

Answer 1

Step 1:

The Curve is , and .

Length of the curve:.Here .

.

Differentiate on each side with respect to .

                  (Since )

.

.

Simpson's rule:

Let be continuous on let be an even integer,

The Simpsons Rule for approximating is given by

where and

Step 2:

Here .

 

 

Answer 2

Continued:

Step 3:

Substitute all above values in Equation (1).

 Arc length of the curve is .

Solution:

Using Simpson's rule, arc length of the curve is .