Evaluate the given integral by making an appropriate change of variables.

The integrand and given boundary for R suggests we should use

u = x - 4y

v = 5x - y

with 0 ≤ u ≤ 3 and 6 ≤ v ≤ 9.

Then

x = (4v - u)/19

y = (v - 5u)/19

and the Jacobian for this transformation is

The integral is then

step-by-step explanation:

it will be a cylinder. with a diameter of 8 and 4 single pieces high