Calcule a integral interada.

Passo 1

Falaaaa ai pessoal tudo blz?

Dado a integral ,

int_0^1 int_0^(1 - x) int_(2 y)^(1 + y^2) x d z d y d x

Passo 2

Resovendo a integral temos,

int_0^1 int_0^(1 - x) x z │_(2 y)^(1 + y^2) d y d x

int_0^1 int_0^(1 - x) x ( 1 + y^2 - 2 y ) d y d x

int_0^1 int_0^(1 - x) x + x y^2 - 2 y x d y d x

int_0^1 x + x (y^3)/(3) - (2 y^2 x)/(2) │_0^(1 - x) d x

int_0^1 x + x ((1 - x)^3)/(3) - (1 - x)^2 x

int_0^1 x + x ((- x^3 + 3 x^2 - 3 x + 1))/(3) - (x^2 - 2 x + 1) . x d x

int_0^1 x - (x^4 + 3 x^3 - 3 x^2 + x)/(3) - x^3 + 2 x^2 - x d x = (1)/(10)

Resposta

(1)/(10)