Question

Graph the curve and find its length.

Answer 1

Step 1:

The functions are and , .

Consider .

Apply derivative on each side with respect to .

Consider .

Apply derivative on each side with respect to .

Step 2:

Find the length of the curve.

Theorem :

If a curve is described by the parametric equations and , then the length of the curve is

The length of the curve is .

Step 3:

Graph :

Graph the curve and .

Solution :

The length of the curve is .

Graph of the curve :