Subbarayan two dimensional integrals x where j x

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Unformatted text preview: m ∫ xi 1 L f ( x)dx = ∫ g (ξ )d ξ 2 −1 Chapter 27 Page 3 G. Subbarayan Two-dimensional integrals ⎡ ∂x ⎢ ∂ξ where [ J ] = ⎢ ⎢ ∂x ⎢ ∂η ⎣ 11 ∫ f ( x, y)dxdy = ∫ ∫ g (ξ ,η ) det[ J ]dξ dη A −1 −1 ∂y ⎤ ∂ξ ⎥ ⎥ ∂y ⎥ ∂η ⎥ ⎦ ⎡ ∂x ⎢ ∂L where [ J ] = ⎢ 1 ⎢ ∂x ⎢ ∂L ⎣2 ∂y ⎤ ∂L1 ⎥ ⎥ ∂y ⎥ ∂L2 ⎥ ⎦ or, in area coordinates 11 ∫ f ( x, y)dxdy = ∫ ∫ g ( L , L ) det[ J ]dL dL 1 A 00 2 1 2 Chapter 27 Page 4 G. Subbarayan x( L1 , L2 ) = L1 X 1 + L2 X 2 + L3 X 3 = L1 X 1 + L2 X 2 + (1 − L1 − L2 ) X 3 y ( L...
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