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Problem 37 Medium Difficulty

Although it is often true that a double integral can be evaluated by using either $d x$ or $d y$ first, sometimes one choice over the other makes the work easier. Evaluate the double integrals in Exercises 37 and 38 in the easiest way possible.
$$\iint_{R} x e^{x y} d x d y ; \quad 0 \leq x \leq 2,0 \leq y \leq 1$$




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