Learn More  Fiveable Community students are already meeting new friends, starting study groups, and sharing tons of opportunities for other high schoolers. Soon the Fiveable Community will be on a totally new platform where you can share, save, and organize your learning links and lead study groups among other students! 🎉  # 9.9 Finding the Area of the Region Bounded by Two Polar Curves

#areabetweencurves

#polar

written by sumi vora

Once you get the hang of finding the area under one curve, finding the area between two curves is pretty simple. Remember from previous units that when you find the area between two curves, you subtract the bottom curve from the top curve. This is the same in polar functions, but instead of subtracting “top minus bottom,” you’ll subtract “outer minus inner.”  If the curves intersect, then you may have to find the area inside the curves by splitting the region.

Example: Let R be the region inside the graph of the polar curve r = 4 and r = 4 + 2sin(2θ) on [0, π]. Find the area of R.  Since the graphs intersect at θ = 2 we can see that when θ < π/2, r = 4 is on top, and when θ > π/2, r = 4+2sin(2θ) is on top. Based on this information, we can construct two integrals: ## Polar Arc Length

There is one last thing you need to know about polar functions: arc length. Finding arc length is pretty straightforward, but you do need to have the formula memorized for the exam.  