(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use the transformationu = 3x + 2yandv = x + 4yto 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.

2. Relevant equations

3. 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

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# Homework Help: Substitution in double integral

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