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

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SUMMARY

The area enclosed by the lemniscate defined by the polar equation r² = -25cos(θ) is calculated to be 25. To find the correct integral setup for this area, the integral formula A = (1/2) ∫ r² dθ is utilized. The values of θ that return to the origin within the interval [0, 2π) are 0 and π, which are essential for determining the limits of integration for the area calculation.

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veronica1999
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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!
 
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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?
 

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