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c10s5 - 2 sin 2 r = Example Find the area of the region...

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10.5 Area and Lengths in Polar Coordinates The area of a circular sector is  2 1 . 2 A r θ = The area of a polar region is [ ] 2 2 1 1 2 2 ( ) or with ( ) b b a a A f d A r d r f θ θ θ θ = = = It can be helpful to graph the functions and to make use of the symmetry in many polar graphs. Example: Find the area of the region bounded by   cos3 12 12 r π π θ θ - = . Example: Find the area of the region bounded by the curve  4 4cos r θ = -  . Example: Find the area of the region bounded by the curve 
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Unformatted text preview: 2 sin 2 r = . Example: Find the area of the region bounded by one loop of the curve 3sin 2 r = . Area Between Curves [ ] [ ] ( 29 2 2 1 2 ( ) ( ) b a A f g d = -∫ Example: Find the area of the region inside the first curve and outside the second curve. 3cos , 2 cos . r r = =-Example: Find the area of the region inside both curves. sin 2 , sin . r r = =...
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