Evaluate the integral by making an appropriate change of variables.
27. ∬R ex + y dA, where R is given by the inequality |x| + |y| ≤ 1
To evaluate: The integral by change of variable method.
The integral is and the region is given by inequality .
Property used: Change of Variable
Change of Variable in double integral is given by, (1)
Definition used: Jacobian transformation
If is the function of and is the function of then,
Obtain the value of .
Find the partial derivative of x and y with respect to u and v. then and and then and .
Substitute the corresponding values in equation (3),
This is in the form of inverse of Jacobian transformation but obtain Jacobian transformation
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