Question

Find the area of one loop of the four-leaved rose r=2sin(2θ)?

Answer 1

Step 1:

The polar equation of the curve is .

The curve is a four leaved 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 in polar form is .

Area of the one loop of polar curve is .

Solution:

Area of the one loop of polar curve is .