Mathematics, 06.03.2021 03:50 asalimanoucha2v
The transformation x=au, y=bv (a>0, b>0) can be rewritten as x/a=u, y/b=v, and hence it maps the curricular region u2+v2≤1 into the elliptical region x2/a2+y2/b2≤1. In these exercises, perform the integration by transforming the elliptical region of integration into a circular region of integration and then evaluating the transformed integral in polar coordinates.
∬R16x2+9y2dA
,where R is the region enclosed by the ellipse
(x2/9)+(y2/16)=1
Answers: 2
which maps the circular region u² + v² ≤ 1 into the elliptical region 
![= \left[\begin{array}{ccc}\dfrac{\partial x}{\partial u}&\dfrac{\partial x}{\partial v}\\\dfrac{\partial y}{\partial u}&\dfrac{\partial y}{\partial v}\\\end{array}\right] \\ \\ \\ \\ = \left[\begin{array}{ccc}3&0\\0&4\\\end{array}\right] \\ \\ \\ = 12](/tpl/images/1174/1799/63e57.png)
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The transformation x=au, y=bv (a>0, b>0) can be rewritten as x/a=u, y/b=v, and hence it maps t...
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