Find the area Inside the graph of Find the area Inside the g

Find the area Inside the graph of

Find the area Inside the graph of r = 2 + cos3 theta

Solution

use this formula

Area = (1/2) r^2 d , Integrate from 0 to 2pi

Area = (1/2)   ( 2+cos3)^2 d Integrate from 0 to 2pi

Area = (1/2)    (4 +cos^2(3) +6cos3) d from 0 to 2pi

after integrating this

Area = ( sin(6)+16sin(3)+54 )/ 12 from 0 to 2pi

Area = [0+0 +54(2pi) ] /12 - 0

Area = 108pi/12

Area = 9pi