Question

Evaluate the integral ∬ ????, where ? is the square with vertices (0,0),(1,1), (2,0), and (1,−1),...

Evaluate the integral ∬ ????, where ? is the square with vertices (0,0),(1,1), (2,0), and (1,−1), by carrying out the following steps:

a. sketch the original region of integration R in the xy-plane and the new region S in the uv-plane using this variable change: ? = ? + ?,? = ? − ?,

b. find the limits of integration for the new integral with respect to u and v,

c. compute the Jacobian,

d. change variables and evaluate the new integral.

Math   Calculus   
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