Calculus with Polar Coordinates Ex. Find all points of intersection of r = 1 – 2cos θ and r = 1.
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Transcript of Calculus with Polar Coordinates Ex. Find all points of intersection of r = 1 – 2cos θ and r = 1.
![Page 1: Calculus with Polar Coordinates Ex. Find all points of intersection of r = 1 – 2cos θ and r = 1.](https://reader030.fdocuments.net/reader030/viewer/2022032803/56649e3b5503460f94b2d996/html5/thumbnails/1.jpg)
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.](https://reader030.fdocuments.net/reader030/viewer/2022032803/56649e3b5503460f94b2d996/html5/thumbnails/2.jpg)
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.](https://reader030.fdocuments.net/reader030/viewer/2022032803/56649e3b5503460f94b2d996/html5/thumbnails/3.jpg)
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.](https://reader030.fdocuments.net/reader030/viewer/2022032803/56649e3b5503460f94b2d996/html5/thumbnails/4.jpg)
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.](https://reader030.fdocuments.net/reader030/viewer/2022032803/56649e3b5503460f94b2d996/html5/thumbnails/5.jpg)
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.](https://reader030.fdocuments.net/reader030/viewer/2022032803/56649e3b5503460f94b2d996/html5/thumbnails/6.jpg)
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.](https://reader030.fdocuments.net/reader030/viewer/2022032803/56649e3b5503460f94b2d996/html5/thumbnails/7.jpg)
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.](https://reader030.fdocuments.net/reader030/viewer/2022032803/56649e3b5503460f94b2d996/html5/thumbnails/8.jpg)
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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