MHB The two values for $\theta$ would be 0 and $\pi$.

[veronica1999]

Question: What is the area enclosed by the lemniscate r² = -25cos(Ѳ)?
The answer is 25.

I can't seem to set up the integral for this question correctly. I know that the area enclosed by a polar curve is obtained by the integral(r²/2) dѲ, but I can't determine what the interval of integration would be.
Help please!

 

[MarkFL]

Let's take a look at a plot of the curve:

View attachment 2452

We want to begin and end at the origin...what two values for $\theta$ on $[0,2\pi)$ will put you at the origin?