Enunciado

Calcule a integral interada.

Passo 1

Falaaaa ai pessoal tudo blz?

Dado a integral ,

int_1^2 int_0^x int_1^(x + x y) x y d z d y d x

Passo 2

Resovendo a integral temos,

int_1^2 int_0^x x y z │_1^(x + x y) d y d x

int_1^2 int_0^x x y (x + x y) - x y ( 1 ) d y d x

int_1^2 int_0^x x^2 + x^2 y + y x + x y^2 - x y d y d x

int_1^2 int_0^x x^2 + x^2 y + x y^2 d y d x

int_1^2 x^2 + x^2 (y^3)/(3) - (2 y^3 x)/(3) │_0^x d x

int_1^2 x^2 x + x^2 (x^2)/(2) + x (x^3)/(3) d x

int_1^2 x^3 + (x^4)/(2) + (x^4)/(3) d x

(x^4)/(4) + (x^5)/(10) + (x^5)/(15) │_1^2 = (107)/(12)

Resposta

(107)/(12)