Use the given transformation to evaluate the integral.
17. ∫∫R x2 dA, where R is the region bounded by the ellipse 9x2 + 4y2 = 36; x = 2u, y = 3v
To evaluate: The integral .
The region R is bounded by the ellipse and ,
Property used: Change of Variable
Change of Variable in double integral is given by,
If is the function of and is the function of then,
Obtain the Jacobian,
Find the partial derivative of x and y with respect to u and v. then and and then and .
From the given integral the function is, and substitute the values of x and y.
Find the boundary by using the given transformation.
The ellipse is the image of
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