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Lecture13_Double_integrals_in_polar_coor

Lecture13_Double_integrals_in_polar_coor - Double Integrals...

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6 Double Integrals in Polar Coordinates The integral over the region R may be calculated by 2 successive integrations using two different orders: The element of area in polar coordinates is given by 2 2 2 ); sin( ); cos( y x r r y r x d dr r dy dx dA + = = = = = θ θ θ with ∫ ∫ ∫∫ ∫ ∫ ∫∫ = = = b a r h r h R g g R rdr d r u d r rd r u rdrd r r f dxdy y x f θ θ θ θ θ θ θ β α θ θ ) ( ) ( ) ( ) ( 2 1 2 1 ) , ( ) , ( ) sin , cos ( ) , ( Å r-first Å θ -first
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