Question

What is the area under the polar curve `f(theta) = theta` over `[0,2pi]`?

Answer 1

The area is given by the formula

#A=1/2 int_(0)^(2pi) f(theta) d(theta)=> A=1/2 int_(0)^(2pi) theta d(theta)=> A=1/4 [theta^2]_0^(2pi)=pi^2#