Question

Find the area of the region enclosed by one loop of the curve.

r = sin 4θ

Answer 1

Step 1:

The curve is  .

Area of the curve enclosed in the first loop is .

Two consecutive values for which is zero in the first loop are .

Now integrate from .

Area enclosed by one of the loop is .

Area of the curve enclosed in the first loop is .

Solution:

Area of the curve enclosed by one loop of the curve  is .