Mathematics, 03.07.2020 14:01 Juicebox18
5) Find the area of the region R that lies inside the cardioid r = 2(1+cos0) and outside the circle r = 3
Answers: 1
 and 
, and then subtract the area of the circle of radius 3 also in between the same limits for the angle 
:![\int\limits^\frac{\pi}{3} _{-\frac{\pi}{3}} \int\limits^{2(1+cos(\theta)}_0 {r\,dr} \, d\theta =\int\limits^\frac{\pi}{3} _{-\frac{\pi}{3}} \frac{4(1+cos(\theta))^2}{2} d\theta =2\,\int\limits^\frac{\pi}{3} _{-\frac{\pi}{3}} 1+2\,cos(\theta)+cos^2(\theta) d\theta=2\,[\theta+2\,sin(\theta)+\frac{1}{2} (\theta+\frac{sin(2\theta)}{2} )]\limits^\frac{\pi}{3} _{-\frac{\pi}{3}}\approx 14.07741](/tpl/images/0700/5655/aae28.png)
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5) Find the area of the region R that lies inside the cardioid r = 2(1+cos0) and outside the circle...
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