( 887, #13) Use the transformation x = 2u, y = 3v to evaluate the integral.

where R is the region bounded by the ellipse

Solution: The region R is the ellipse

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Substituting x = 2u and y = 3v in the equation for the ellipse we get:

Thus the set S describes a disk of radius 1.

The Jacobian is:

Thus evaluating the integral we have:

by: nl