Related Rates | Volume Integration | Polar Calculus | Integration by Parts | Quiz

**Polar Calculus**

**Differentiating polar equations.**

Since most of our functions will be given as R(theta), it takes additional steps to find the slope of the tangent line since we want dy/dx. To find dy/dx, we can first find dy/dtheta and then divide by dx/dtheta, effectively leaving dy/dx.

Example 1: Find the slope of the line tangent to at

Since we want to find , we will need to find

Now we substitute in and find that , when .

**Finding areas of polar equations.**

Unlike finding the area in a cartesian system, finding the area in a polar system means that the area will be a sum of the sectors swept out instead of a sum of rectangles.

To find the area over an interval (a,b) it is .

Example 2: Find the area of the region

Since the period of this function is just , we can simply integrate from 0 to .

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