1. Calculus with Polar Coordinates Ex. Find all points of intersection of r = 1 – 2cos θ and r = 1.

2. The area bounded by r = f (θ), α ≤ θ ≤ β is

3. Ex. Find the area of one petal of r = 3cos 3θ

4. Ex. Find the area between the inner and outer loops of the curve r = 1 – 2sin 3θ

5. Ex. Find the area inside r = 3sin θ and outside r = 1 + sin θ.

6. The arc length of the curve r = f (θ), α ≤ θ ≤ β is

7. Ex. Find the length of the curve given by r = 1 + sin θ

8. Pract. 1. Find the area of one loop of r = cos 2θ. 2. Find the area of the region that lies inside r = 3sin θ and outside r = 1 + sin θ. 3. Set up an integral to find the length of the curve r = θ for 0 ≤ θ ≤ 2π.