10.4 Areas and Arc Lengths in Polar Coordinates

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6 Terms

1
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dA =

(theta / 2π) (πr²) = (1/2) r² (theta)

2
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A (bounds a, b) =

int (bounds a, b) ( (1/2) f(theta)²) dtheta

3
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dℓ =

dtheta sqrt( (dx/dtheta)² + (dy/dtheta)² )

4
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dx/dtheta = 

f’(theta) cos(theta) - f(theta) sin(theta)

5
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dy/dtheta =

f’(theta) sin(theta) + f(theta) cos(theta)

6
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ℓ =

int (bounds theta1, theta2) (sqrt( (f(theta)²+ (f’(theta)²) dtheta )