Question

Find the area of the region.

one petal of r = sin 2θ

Answer 1

Step 1:

The polar curve is .

The curve is a four-leaved rose.

Four loops of the rose are determined by substituting .

General solution of sine function  is .

For first loop, substitute in the above.

First loop of the curve  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 .