## Related questions with answers

Question

Use the given transformation to evaluate the integral. double integral (x-3y)dA, where R is the triangular region with vertices (0, 0), (2, 1) and (1, 2); x=2u+v, y=u+2v

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1 of 8Answered 1 year ago

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1 of 6**Theorem:** Change of Variables in a Double Integral.

$\iint_R f\left(x, \ y\right) \ dA=\iint_S f\left(x\left(u, \ v\right), \ y\left(u, \ v\right)\right) \ \Bigg| \frac{\partial \left(x, \ y\right)}{\partial \left(u, \ v\right)} \Bigg| \ du \ dv.$

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1 of 4Formula for the Jacobian:

$\begin{align*} \frac{\partial\lparen x,y\rparen}{\partial\lparen u,v\rparen}=\begin{vmatrix} \frac{\partial x}{\partial u}&\frac{\partial x}{\partial v}\\ \frac{\partial y}{\partial u}&\frac{\partial y}{\partial v} \end{vmatrix}\end{align*}$

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