Evaluate the double integral ∬D6xydA, where D is the triangular region with vertices (0,0), (1,2), and (0,3).

Answer 1

∫∫_D6xydA = ∫₀¹6x∫_2x^3-xydx = 3∫₀¹xy²_2x^3-xdx = 3∫₀¹(9 - 6x + x² - 4x²)xdx = (9x²/2 - 2x³ - 3x⁴/4)₀¹ = 9/2 - 2 - 3/4 =

7/4 = 1.75