Problems

In Problems 1-13, find the area of the regions bounded by the following curves in polar coordinates.

14            Find the area of the region inside the curve r = 2 cos θ and outside the curve r = 1.

15            Find the area of the region inside the curve r = 1 sin θ and above the line r = 3/2 csc θ.

16            Find the area of the region inside the spiral r = θ, 0 ≤ θ ≤ 2π.

17            Find the area of the region inside the spiral r = √θ, 0 ≤ θ ≤ 2π.

18            Find the area of the region inside both of the curves r = √3 cos θ, r = sin θ.

19            Find the area of the region inside both of the curves r = 1 - cos θ, r = cos θ.

20            The center of a circle of radius one is on the circumference of a circle of radius two. Find the area of the region inside both circles.

21            Find a formula for the area of the region between the curves r = f(θ) and r = g(θ), a ≤ θ ≤ b, when 0 ≤ f(θ) ≤ g(θ).