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Area under Polar curve question!!! 10 Points!?
Find the area inside the cardidoid r = 1 + cos(theta) and outside the circle r = 1!?
2 Answers
- 7 years ago
r=1 + cos(t)=1 and t= pi/2 and 3pi/2
area of a polar curve = 1/2 the integral of R^2 -r^2
integral of (cost+1)^2- 1) from 0 to pi/2=
integral cost^2+2cost from 0 to pi/2
integral (1+cos2t)/2+2cost from o to pi/2=
1/2t + 1/4 sint + 2sint for o to pi/2=
pi/4 +2
- ted sLv 77 years ago
NOTE : " P A " dropped the [ 2 ] in integrating cos 2t..and the domain should be [ - π /2 , π / 2 ]
but doubling the integral over [ 0 , π /2 ] works
