1.$\displaystyle \int_{\bold{R}} xy \ dx \ dy, \ \ \ R = \text{triangle with vertices at} \ (1,0), (2,2) \ \text{and} \ (1,2) $.

Is this equaled to $\displaystyle \int\limits_{1}^{2} \int\limits_{2x-2}^{2} xy \ dy \ dx = -\frac{7}{12}$?

2.$\displaystyle \int_{\bold{R}} e^{xy} \ dx \ dy, \ \ \ R = \{(x,y) \ | \ 0 \leq x \leq 1 + (\log y)/y \}, 2 \leq y \leq 3 \} $.

Here I am assuming that $\displaystyle \log y = \ln y $.

So $\displaystyle 0 \leq x \leq 1 + (\log 3)/3 $ and $\displaystyle 2 \leq y \leq 3 $.

So is the integral: $\displaystyle \int\limits_{0}^{1 + (\log 3)/3} \int\limits_{2}^{3} e^{xy} \ dy \ dx $?