Word Count : 478

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First, describe the region (D): [ D = {(x, y) : x \ge 0, y \ge 0, x + y \le 4}. ] This is a right triangle in the first quadrant with vertices at ((0,0)), ((4,0)), and ((0,4)). Type I (x-bounds constant, y-bounds variable): For Type I, (x) is the independent variable: (0 \le x \le 4), and for each (x), (y) ranges from (0) to (4 - x). [ \iint_D e^{2x + 3y} , dy , dx = \int_0^4 \left( \int_0^{4-x} e^{2x + 3y} , dy \right) dx ] Integrate with respect to _________ __________ ____ _________ __________ ___ ___ __________ __________ ____ ________.
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