- #1
DWill
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Homework Statement
Use the transformation u = 3x + 2y and v = x + 4y to evaluate:
The double integral of (3x^2 + 14xy + 8y^2) dx dy for the region R in the first quadrant bounded by the lines y = -(3/2)x + 1, y = -(3/2)x + 3, y = -(1/4)x, and y = (-1/4)x + 1.
Homework Equations
The Attempt at a Solution
I first wrote the equations for x and y in terms of u and v and got:
x = (2u - v)/5, y = (3v - u)/10
Then I solved for the Jacobian and got 1/10. Next I saw that the region R has the following boundaries:
x = 2/3 - (2/3)y
x = 2 - (2/3)y
y = 0
Plugging in the equations I got earlier for x and y, I get the equivalent in terms of u and v:
u = 2
u = 6
v = u/3
So I set up my integral now like this:
Double integral of (u * v) * (1/10) dv du, with 2 <= u <= 6, and 0 <= v <= u/3. Solving this I get the answer 16/9, while the correct answer is 64/5. Which part(s) did I do wrong here? thanks