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

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#

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The area under the polar curve ( f(\theta) = \theta ) over the interval ([0, 2\pi]) is (\pi^2).

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