If is continuous, the average value of the polar coordinate r over the curve r = (), , with respect

If ƒ is continuous, the average value of the polar coordinate r over the curve r = ƒ(θ), α ≤ θ ≤ β, with respect to θ is given by the formula

Use this formula to find the average value of r with respect to θ over the following curves (a > 0).

a. The cardioid r = a(1 - cos θ)

b. The circle r = a

c. The circle r = a cos θ, -π/2 ≤ θ ≤ π/2

1 Eptal r f(0) .