Mathematics, 16.01.2020 02:31 malikfitzgerald7392
(1 point) evaluate the double integral ∬d4xyda, where d is the triangular region with vertices (0,0), (1,2), and (0,3).
Answers: 3
![\int\limits^1_0\int\limits_{2x}^{3-x}4xy\:dydx=\int\limits^1_0 2xy^2|_{2x}^{3-x}\:dx=\int\limits^1_0 2x[(3-x)^2-(2x)^2]\:dx=\\\\=\int\limits^1_0 2x(9-6x-3x^2)\:dx=6\int\limits^1_0 (3x-2x^2-x^3)\:dx=\\\\=6(\frac{3}{2}x^2-\frac{2}{3}x^3-\frac{1}{4}x^4)|^1_0=6(\frac{3}{2}-\frac{2}{3}-\frac{1}{4})=\frac{7}{2}](/tpl/images/0457/0277/07541.png)
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(1 point) evaluate the double integral ∬d4xyda, where d is the triangular region with vertices (0,0)...
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