Question

 Find the exact length of the polar curve.

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.

Consider .

When .

When .

.

Substitute corresponding values in L.

The exact length of curve is

Solution :

The exact length of curve is