I see what you're saying, but I still disagree. To find the area of that loop, we must integrate between the two values of x for which r = 0. They are 0 and pi/3. I'm pretty certain that the area under the graph will not be counted (only the enclosed area will be counted).
Anyway, I had my final exam today and I think it went really well!
I even had time to count up what I definately got right, which I think is about 90%. So I'm very happy right now! The only thing I know I got wrong was: "sinh(x) + 2cosh(x) = 8. Solve for x". I know this is easy, but I got all the way to finding the roots of a quadratic when instead of dividing by 10 (in the quadratic formula), I divided by 2!
Thanks for the help, Jetru.
: By the way, your calulator looks very similiar to mine, its not the "CFX-9850G PLUS" by any chance?