Question

Calcule o valor da integral... onde R = [0,3] x [1,2].

Answer 1

$\displaystyle\sf{\int_{0}^{3}\int_{1}^{2}x^2y~dy~dx }$

$\displaystyle\sf{\dfrac{1}{2}\int_{0}^{3}x^2y^2\Bigg|_{1}^{2}dx}\\\displaystyle\sf{\dfrac{1}{2}\int_{0}^{3}x^2\cdot[2^2-1^2]}\\\displaystyle\sf{\dfrac{3}{2}\int_{0}^{3}x^2dx=\dfrac{1}{2}x^3\Bigg|_{0}^3}\\\sf{\dfrac{1}{2}\cdot3^3=\dfrac{27}{2}}$