Use the given transformation to evaluate the integral.
20. ∫∫R y2 dA, where R is the region bounded by the curves xy = 1, xy = 2, xy2 = 2; u = xy, v = xy2. Illustrate by using a graphing calculator or computer to draw R.
To evaluate: The integral .
The region R bounded by the curves , , , 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,
Write u and v in terms of x and y respectively.
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
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