Question

Find the length of the curve over the given interval.

Polar equation                                                       Interval

Answer 1

Step 1 :

Arc length :

The length of a curve with polar equation is

.

Step 2 :

The polar equation is .

Apply derivative on each side with respect to .

The exact length of the polar curve is .

Substitute and  in above equation.

Solution :

The exact length of curve is .