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

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

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

Calculus with Polar Coordinates

Ex. Find all points of intersection of r = 1 – 2cos θ and r = 1.

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

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

212A f d

Page 3: Calculus with Polar Coordinates Ex. Find all points of intersection of r = 1 – 2cos θ and r = 1

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

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Page 4: Calculus with Polar Coordinates Ex. Find all points of intersection of r = 1 – 2cos θ and r = 1

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

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Page 5: Calculus with Polar Coordinates Ex. Find all points of intersection of r = 1 – 2cos θ and r = 1

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

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Page 6: Calculus with Polar Coordinates Ex. Find all points of intersection of r = 1 – 2cos θ and r = 1

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

2 2s f f d

Page 7: Calculus with Polar Coordinates Ex. Find all points of intersection of r = 1 – 2cos θ and r = 1

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

Page 8: Calculus with Polar Coordinates Ex. Find all points of intersection of r = 1 – 2cos θ and r = 1

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.

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