find-the-area-of-the-region-enclosed-by-the-polar-curve-r-4-2-cos-

Question Number 87146 by john santu last updated on 03/Apr/20

find the area of the region

enclosed by the polar curve

r = 4 + 2 \cos θ ?

Answered by jagoll last updated on 03/Apr/20

Commented by jagoll last updated on 03/Apr/20

area = \underset{0}{\int^{2 π}} \frac{1}{2} r^{2} d θ

= \frac{1}{2} \int \underset{0}{\overset{2 π}{}} {(4 + 2 \cos θ)}^{2} d θ

= \frac{1}{2} \underset{0}{\int^{2 π}} (16 + 16 \cos θ + 4 (\frac{1}{2} + \frac{1}{2} \cos 2 θ)) d θ

Facebook Tweet Pin