Finding Area Between Polar Curves - Help Understanding Bounding

In summary, the conversation is about finding the area between two polar curves. The speaker is having trouble with the bounds and is seeking help to better understand how to bound the curves. They also mention a specific problem they are struggling with and provide their work. Another person chimes in and advises that different bounds are needed for each curve and provides an expression for finding the area. The original speaker thanks them for their help.
  • #1
itzela
34
0
I am having trouble finding the area between 2 polar curves... I have the procedure down, but the bounds are throwing me off. Any help with understanding how to bound would be great appreciated!

I have attatched one problem that I am having hard time with and the work I have done. I know that I am doing something wrong because I am getting a negative number for an area (which shouldn't be).
 

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  • #2
You can't write that as one integral in that way. The Functions do not respond to the parameters the same way, different bounds are needed for each.
[tex]\frac{A}{2}=\frac{1}{2}\int_{\frac{\pi}{3}}^{\pi}(1+\cos(\theta))^2 d\theta - \frac{1}{2}\int_{\frac{\pi}{3}}^{\frac{\pi}{2}}(3\cos(\theta))^2 d\theta[/tex]
 
Last edited:
  • #3
Thanks :smile:
After working on it for a little while i arrived at the same expression... and i was a little unsure about it, but you confirmed it!
 

1. What is meant by "finding area between polar curves"?

When working with polar coordinates, it is possible to have two or more polar curves on the same graph. Finding the area between these curves means finding the area of the region that is enclosed by these curves.

2. How do I determine the boundaries for finding the area between polar curves?

The boundaries for finding the area between polar curves are the points where the curves intersect. These points can be found by setting the equations of the curves equal to each other and solving for the values of theta.

3. Can the area between polar curves be negative?

No, the area between polar curves cannot be negative. The area represents a physical quantity and therefore must be positive. If you get a negative value for the area, it may be an indication that you have set up the integrals incorrectly or that you have chosen the wrong boundaries.

4. What is the difference between finding the area between polar curves and finding the area under a polar curve?

The area between polar curves involves finding the area of the region enclosed by two or more curves, while finding the area under a polar curve involves finding the area of the region between a single curve and the origin.

5. Are there any special techniques for finding the area between polar curves?

Yes, there are a few techniques that can be used to find the area between polar curves. These include using symmetry to reduce the number of integrals, using trigonometric identities to simplify the integrand, and using the formula for the area of a sector to calculate the area of a small region of the curve.

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