Sketch the polar curves r = 6 sin θ and r = 2+ 2 sin θ, then set up an integral that represents the area inside r = 6 sin θ and outside r = 2 + 2 sin θ. Do not evaluate your integral.

Answer :

Answer:

Step-by-step explanation:

Given are two polar curves as [tex]r = 6 sin θ and r = 2+ 2 sin θ[/tex]

Let us find the point/s of intersection

Eliminate r to get

[tex]6 sin θ = 2+ 2 sin θ\\sin\theta = 0.5\\\theta = 30, 150[/tex]

[tex]r=6sin 30 = 3[/tex]

Thus we find that area outside II curve and inside first curve would be

[tex]\int {\frac{r^2}{2} } \, d\theta \\ =\int{\frac{36sin^2 \theta - (2+2sin\theta)^2 }{2} } \, d\theta[/tex] where lower limit is 30 degrees and 150 degrees.

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