Urgent help please

[junhoma]

Evaluate double integral y^2(y-2x)cos(y-2x) dA over the triangular region R with vertices (0,0), (1,2) and (0,2) by making appropriate substitutions of the form u=Ax+By and v=cx+Dy.
Please help me to solve this problem.

 

[Deleted member 4993]

Evaluate double integral y^2(y-2x)cos(y-2x) dA over the triangular region R with vertices (0,0), (1,2) and (0,2) by making appropriate substitutions of the form u=Ax+By and v=cx+Dy.
Please help me to solve this problem.

First draw a sketch of the triangular region and determine the limits of integration.

Please show us your work, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[galactus]

Try \(\displaystyle u=y-2x, \;\ v=2x\)

This then gives \(\displaystyle y=u+v, \;\ x=\frac{v}{2}\)

These subs create new limits of integration

\(\displaystyle u=0, \;\ u=2-v, \;\ v=0, \;\ v=2\)

Now, find the determinant of the partials and proceed.