Area Between Polar Curves

 

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Area between two polar curves

If you need to find the area between two polar curves, just as you did on a cartesian coordinate system you’ll need to first find the points at which the two graphs intersect one another, and these will be your limits of integration. Remember how, to find the area between the curves, you had to subtract the lower curve from the upper curve? Well, in polar coordinates, you’ll be subtracting the inner curve from the outer curve.

Use this formula to find the area between two polar curves.

A=\int_{\alpha}^{\beta}\frac{1}{2}(r_{\mbox{outer}})^2-(r_{\mbox{inner}})^2\ d\theta

 

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