Solved: Double integrals—transformation given To evaluate

QUESTION:

Double integrals-transformation given To evaluate the following integrals carry out these steps.

a. Sketch the original region of imegration R in the xy-plane and the new region S in the uv-plane using the given change of variables.

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,

\(\iint_{R} x^{2} y d A\) where \(R=\{(x, y): 0 \leq x \leq 2, x \leq y \leq x+4\}\); use use x = 2u, y = 4v + Zu.