Find area of region?

Question

one petal of r=cos 5 theta

Answer 1

One petal extends from -pi/10 to +pi/10, so we integrate the expression from
theta = -pi/10
to
theta = pi/10.

integral(cos(5*theta),theta,-pi/10,pi/10)
= 1/5 * sin(5*theta), evaluated from -pi/10 to pi/10
= (1/5) - (-1/5)
= 1/5 + 1/5
= 2/5

The area of the petal is 2/5.

Answer 2

it is part of application of integral calculus..its difficult here to show the calculations...

however i suggest you to view this site...
http://www.ltcconline.net/greenl/courses/107/premid2/polarea.htm

i hope this thing can help...