Answer to Question #282409 in Calculus for james

Question

Find the area enclosed by the curve r = 5cosθ

Answer 1

Solution:

Assuming that we are dealing with polar coordinates, the curve :

$$r=5cos\theta$$

for 0 < θ < π traces out a circle of radius $\frac{5}{2}$ centered at $x=\frac{5}{2}$ , y=0. For π < θ < 2π the same circle is repeated. The area within the circle is, therefore,

$$\pi(\frac{5}{2})^2=\frac{25\pi}{4}$$