13.4 Polar Coordinates

# 13.4 Polar Coordinates -   1 3.4  P o l a r  C o o r...

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Unformatted text preview:   1 3 .4  P o l a r  C o o r d in a t e s     x = r cosθ y = r sin θ y tan θ = x                              x 2 + y 2 = r2                         ∫∫ f ( x, y ) dA = ∫ β α R ∫ b a f ( r cos θ, r sin θ ) r drdθ α ≤ θ ≤ β and a ≤ r ≤ b .    Ex.  Let R be the region shown below.  3 2 1 -3 -2 -1 1 2 3 -1 -2   -3         Ex.  2 1 -2 -1 1 2 -1 -2       where                    1 ∫∫ 1− x 2 1 − x 2 − y 2 dydx  by  Ex.  Evaluate  0 0 changing to polar coordinates.                                      1 ∫∫ 2− x dydx Ex. Set up an integral to evaluate  0 x  by changing  to polar coordinates.                      Ex. Find the area inside  r = 4 cosθ  and outside r = 2.                                  Do: Set up an integral to evaluate  0 ∫∫ −2 0 4 −y 2 x 2 + y 2 dxdy  by changing to polar  coordinates.                     ...
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## This note was uploaded on 10/02/2011 for the course AERO 1234 at Virginia Tech.

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