Section 12.6 – Area and Arclength in Polar Coordinates

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Presentation transcript:

Section 12.6 – Area and Arclength in Polar Coordinates 12.2

Integrals in Polar Coordinates Area of a Polar Curve: 12.2

A graphic of the area inside one loop of the curve r = 2 Sin(3t) http://clem.mscd.edu/~talmanl/MOOVs/SimplePolarArea/SimplePolarArea.MOV A graphic of the area inside one loop of the curve r = 2 Sin(3t) but outside of the circle r = 1 Calculus@Internet A graphic of the area inside the curve r = 1 + Cos(2t) but outside the curve r = Cos(t). http://clem.mscd.edu/~talmanl/MOOVs/HardPolarAreaI/HardPolarAreaI.MOV

The total area of the region enclosed NO CALCULATOR by the polar graph of is

NO CALCULATOR

NO CALCULATOR: Find the area of the region inside the circle r = 4 and outside

CALCULATOR REQUIRED The area of the region enclosed by the graph of the polar curve is 4.712 9.424 18.849 37.699 75.398

CALCULATOR REQUIRED The approximate total area of the region enclosed by the polar graph of is: 0.393 0.785 1.178 1.571 1.873

CALCULATOR REQUIRED Set up to definite integral to find the area inside the smaller loop of

CALCULATOR REQUIRED Find the area inside

Length of an Arc in Polar Coordinates

CALCULATOR REQUIRED

NO CALCULATOR

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