Question

Use Simpson’s Rule with n = 6 to estimate the length of the curve .

Answer 1

Step 1:

The parametric equations of the curve are .

Length of the curve with parametric equations is .

Differentiate with respect to .

Differentiate with respect to .

Substitute , and limits of in formula.

Simpsons rule:

Let be continuous on , let be an even integer,

The Simpsons Rule for approximating   is given by

,

where and

Here .

Answer 2

Step 1:

The parametric equations of the curve are .

Length of the curve with parametric equations is .

Differentiate with respect to .

Differentiate with respect to .

Substitute , and limits of in formula.

Simpsons rule:

Let be continuous on , let be an even integer,

The Simpsons Rule for approximating   is given by

,

where and

Here .

Answer 3

Continued:

Step 2:

Substitute above values in Simpsons formula.

Solution:

Arc length of the curve is .