Homework Help: Calc Jacobian

Posted by Rob on Monday, December 4, 2006 at 3:41am.

Thanks

"I know that the xy region is the line x=y y=0 and y=1- x/2)"

It is helpful to rewrite the region in the x-y plane by specifying the three lines and the endpoints, i.e. the points where they intersect.

If you insert these points in the formula for U and V you obtain the vertices in the U-V plane.

E.g., the line x = y maps to the line
V = 0. But in the x-y plane this line is bounded by the "end points" (x=0,y=0) and (x=2/3,y=2/3) which in the U-V plane has coordinates (U = 0, V = 0) and (U = 2, V = 0) respectively.

I need to find out how to solve this integral with the indicated changes.

int.[0 to 2/3]int[y to 2-2y]
(x+2y)e^(y-x)
dxdy

u=x+2y v=x-y

I know that the xy region is the line x=y y=0 and y=1- x/2)

but when I make the changes, I don't get a new region bounded by graphs.

Can anyone see a way to solve this one?

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