Step 1:

The polar equation of the curve is .

The curve is sixteen petal rose.

Interval one loop of the rose is determined by substituting .

General solution of sine function  is .

For first loop, substitute  in the above solution.

First loop of the curve is observed in the interval  .

Step 2:

Area of the curve for one loop in polar form is .

Area of the curve in polar form for one loop is .

The curve consist of 16 loops then area of the  curve is

The curve consist of 16 loops then area of the  curve is .

Solution:

The curve consist of 16 loops then area of the  curve is .