Question

Calcule a integral dupla ∫∫R xy.dA, sendo que R = (x,y), onde {(x,y) | 0 ≤ x ≤ 2,1 ≤ y ≤ 2 }

Answer 1

Olá!

$\displaystyle\int_0^2\int_1^2xy\;dydx=\int_0^2x\left(\int_1^2ydy\right)dx=\int_0^2x\left(\dfrac{y^2}{2}\right)\bigg{|}_{y=1}^{y=2}\;dx = \\ \\ \\ \int_0^2x\left(\dfrac{4}{2}-\dfrac{1}{2}\right)dx=\dfrac{3}{2}\int_0^2x\;dx=\dfrac{3}{2}\left(\dfrac{x^2}{2}\right)\bigg{|}_{x=0}^{x=2}=\dfrac{3}{2}\left(\dfrac{4}{2}-0\right)=\dfrac{3}{2}\cdot 2 = \\ \\ \\ = 3.$

Bons estudos!

Answer 2

Resposta:

A alternativa correta é:

a. -12

Explicação passo-a-passo: