Question

HELP pleaseeeee (2) somente feras

Answer 1

$\int\limits^2_0 \ \int\limits^2_1 {(2x \ - \ y)} \, dx \ dy$


Integrando em relação a "x":

$\int\limits^2_0 {(\frac{2x^2}{2} \ - \ xy)]^2_1 \, \ dy$

$\int\limits^2_0 {(x^2 \ - \ xy)]^2_1 \, \ dy$


Substituindo "x":


$\int\limits^2_0 {((2)^2 \ - \ (2).y) \ - \ ((1)^2 \ - \ (1).y)\, \ dy$

$\int\limits^2_0 {(4 \ - \ 2y) \ - \ (1 \ - \ y)\, \ dy$

$\int\limits^2_0 {4 \ - \ 2y \ - \ 1 \ + \ y \, \ dy$

$\int\limits^2_0 {3 \ - \ y \, \ dy$


Integrando em relação a "y":

$\int\limits^2_0 {(-y \ + \ 3) \, \ dy$

$(\frac{-y^2}{2} \ + \ 3y) \ ]^2_0$


Substituindo "y":


$(\frac{-(2)^2}{2} \ + \ 3 . (2)) \ - \ (\frac{-(0)^2}{2} \ + \ 3 . (0))$

$(\frac{-(4)}{2} \ + \ 6) \ - \ (\frac{-(0)}{2} \ + \ 0)$

 $(\frac{-4}{2} \ + \ 6) \ - \ (\frac{0}{2} \ + \ 0)$

$(-2 \ + \ 6) \ - \ (0 \ + \ 0)$

$4 - 0 = \boxed{\bold{4}}$