Calculus III - Lab 1a:
Polar Equations

Polar coordinates

Intersections of 2 graphs

Graph the following and find all intersection points of the 2 graphs:
	r = 2  sin (3  θ)
	r = 2 - 3  sin θ

Area between 2 graphs

Find the area of the shaded region a in the graph below numerically (these are the graphs from the previous section).

Find the area of shaded region b in this graph.  (Hint:  pay careful attention to your limits of integration.)

Arc length

Find the total arc length around the graph of r(θ) = 2  sin 3  θ.  Warning:  Do NOT try to do this integral exactly (try it just for grins if you have some time to waste).  Use the command NIntegrate instead (look it up in the Help system if you don't know how to use it).