Change of Variables in Multiple Ingegrals; Jacobian

[kstephens91]

Use the transformation u=x+y, v=3x-2y to find the area of the region enclosed by x+y=1, x+y=2, 3x-2y=2, 3x-2y=5. So far I have that the Jacobian is 5, but I don't understand how to find the limits of integration and I don't know what to integrate.

 

[Deleted member 4993]

Use the transformation u=x+y, v=3x-2y to find the area of the region enclosed by x+y=1, x+y=2, 3x-2y=2, 3x-2y=5. So far I have that the Jacobian is 5, but I don't understand how to find the limits of integration and I don't know what to integrate.

Look at those graphs carefully. In the transformed system those are u = 1, u = 2 , v = 2 and v = 5.

What does that look like?

What would be your limits?

 

[kstephens91]

Got it! Thank you.

 

[galactus]

Here is the region. The balck square is the original and the red one is the transformation.