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I need to solve a double integral and I have no idea what to change the variables to:

[tex] \iint_{R} \cos ( \frac{y-x}{y+x}) \ dA [/tex]

[tex] R=\{(x,y) \mid \ -x+1 \leq y \leq -x+2, 1 \leq x \leq 2 \}

[/tex]

I tried to set [itex] u=y-x [/itex] and [itex]v=y+x[/itex], but I still can't solve the resulting integral. I also tried setting [itex] v + u= \frac{y-x}{y+x} [/itex] and differentiating implicitly when finding the Jacobian, but the Jacobian turns out to be zero.

[tex] \iint_{R} \cos ( \frac{y-x}{y+x}) \ dA [/tex]

[tex] R=\{(x,y) \mid \ -x+1 \leq y \leq -x+2, 1 \leq x \leq 2 \}

[/tex]

I tried to set [itex] u=y-x [/itex] and [itex]v=y+x[/itex], but I still can't solve the resulting integral. I also tried setting [itex] v + u= \frac{y-x}{y+x} [/itex] and differentiating implicitly when finding the Jacobian, but the Jacobian turns out to be zero.

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