16. Parametric Equations & Polar Coordinates

41–44. Intersection points and area  Find all the intersection points of the following curves. Find the area of the entire region that lies within both curves

r = 1 + sin θ and r = 1 + cos θ

45–60. Areas of regions Find the area of the following regions.

The region outside the circle r = 1/2 and inside the circle r = cos θ

45–60. Areas of regions Find the area of the following regions.

The region inside the curve r = √(cos θ) and inside the circle r = 1/√2 in the first quadrant

45–60. Areas of regions Find the area of the following regions.

The region inside one leaf of the rose r = cos 5θ

45–60. Areas of regions Find the area of the following regions.

The region inside the rose r = 4 sin 2θ and inside the circle r = 2

45–60. Areas of regions Find the area of the following regions.

The region common to the circles r = 2 sin θ and r = 1

45–60. Areas of regions Find the area of the following regions.

The region inside the outer loop but outside the inner loop of the limaçon r = 3 - 6 sin θ

45–60. Areas of regions Find the area of the following regions.

The region inside the lemniscate r² = 6 sin 2θ

45–60. Areas of regions Find the area of the following regions.

The region inside the limaçon r = 4 - 2 cos θ

63–74. Arc length of polar curves Find the length of the following polar curves.

The complete circle r = a sin θ, where a > 0

63–74. Arc length of polar curves Find the length of the following polar curves.

The spiral r = θ², for 0 ≤ θ ≤ 2π

63–74. Arc length of polar curves Find the length of the following polar curves.

The complete cardioid r = 4 + 4 sin θ

63–74. Arc length of polar curves Find the length of the following polar curves.

The curve r = sin³(θ/3), for 0 ≤ θ ≤ π/2

63–74. Arc length of polar curves Find the length of the following polar curves.

{Use of Tech} The complete limaçon r=4−2cosθ

63–74. Arc length of polar curves Find the length of the following polar curves.

{Use of Tech} The complete limaçon r=4−2cosθ