TBIL-Calc Polar area (CO6)

Section 7.6 Polar area (CO6)

The area of the “fan-shaped” region between the pole and

r = f (θ)

as the angle

θ

ranges from

α

β

is given by

\int_{θ = α}^{θ = β} \frac{r^{2}}{2} d θ .

Find an integral computing the area of the region defined by

0 \leq r \leq - \cos (θ) + 5

and

π / 2 \leq θ \leq 3 π / 4 .

Find the area enclosed by the cardioid

r = 2 (1 + \cos (θ) .

Find the area enclosed by one loop of the 4-petaled rose

r = \cos (2 θ) .