Question

intregal dupla! ∫¹₋₂∫³₀ $x^{2} y - 2xy dxdy$
me ajudem? já fiz ela várias vezes

Answer 1

$\displaystyle\int_{-2}^1\int_0^3 (x^2y-2xy)\,dx\,dy\\\\\\ =\int_{-2}^1\int_0^3 y\cdot (x^2-2x)\,dx\,dy\\\\\\ =\int_{-2}^1 y\cdot\left.\left(\dfrac{x^3}{3}-x^2 \right )\right|_0^3\,dy\\\\\\ =\int_{-2}^1 y\cdot\left[\left(\dfrac{3^3}{3}-3^2 \right )-\left(\dfrac{0^3}{3}-0^2 \right ) \right ]dy$

$=\displaystyle\int_{-2}^1 y\cdot0\,dy\\\\\\ =\int_{-2}^1 0\,dy\\\\\\ =0$