This sketch allows a brief look at the mechanism of polar integration. The concept is essentially identical to integration with Riemann sums in Cartesian coordinates, but with wedges instead of rectangles. The polar setting brings up some novel facets of the concept of integration. For example, the integral area can overlap itself (see the page of this sketch dealing with the Archimedes Spiral). The construction was tricky, but I recommend it for the experience with the polar coordinates. The theta-interval and the number of sub-intervals are both easily changed to highlight the simplicity and precision of this process as could not be conveyed by a stationary picture.
Keywords: polar integration, polar integral, polar calculus, limacon, cardioid