Question

Resolva a integral dupla 0 int 2 1 int 2 (2x-y)dxdy

Answer 1

$\int\limits^{2}_{0} \int\limits^{2}_{1} \left(2x-y\right)dxdy$

resolvendo a primeira

$\int\limits^{2}_{1} \left(2x-y\right)dx = \left \frac{2x^2}{2} -yx\right|^2_1 = (2^2-2y) - (1^2-1y) = 3-y$

fincando
$\int\limits^{2}_{0} \left(3-y\right)dx= \left 3y- \frac{y^2}{2}\right |^2_0 = (3*2- \frac{2^2}{2})-0 = 4$

.
$\int\limits^{2}_{0} \int\limits^{2}_{1} \left(2x-y\right)dxdy =4$