Evaluating a Double Integral Using a Change of Variables In Exercises 17-22, use the indicated change of variables to evaluate the double integral.
To calculate: The value of double integral using the indicated change of variables.
Given: The provided double integral
The equations, and .
The following graph:
With the help of Jacobian’s formula
And change of variables for double integrals is given as
Calculation: Find the value of the Jacobian as shown below.
Put different values of x and y coordinates from the given graph and replace them in the given 2 equations.
Substitute to get,
In the same way, substitute,
Thus, different values of u and are:
The graph obtained is,
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