Question

Determine the area of the inner loop of the polar curve r = 1 − 2 sin (θ).

Answer 1

Is this the right setup?

Answer 2

Where r_1=1-2sin(theta)

Answer 3

@jim_thompson5910 or @Abhisar please help

Answer 4

So we need to find when r=0 when theta is between 0 and 2pi
So you have 1/2=sin(theta)
which is when you said theta=5pi/6 or pi/6
So I think your limits are right

Answer 5

I get \(\pi - \dfrac{3}{2}\sqrt{3}\). Why do you doubt?

Answer 6

I was just checking to make sure @tkhunny