Question

O volume do sólido compreendido pela superfície z = x^2 e os planos x = 0, x = 2, y = 3, y = 0 e z = 0

Answer 1

             $\displaystyle V=\int_{0}^{2}\int_{0}^{3}\int_{0}^{x^2}dz\,dy\,dx\\ \\ \\ V=\int_{0}^{2}\int_{0}^{3}\left(\int_{0}^{x^2}dz\right)\,dy\,dx\\ \\ \\ V=\int_{0}^{2}\int_{0}^{3}x^2\,dy\,dx\\ \\ \\ V=\int_{0}^{2}x^2\left(\int_{0}^{3}\,dy\right)\,dx\\ \\ \\ V=\int_{0}^{2}3x^2\,dx\\ \\ \\ V=\left.\left(x^3\right)\right|_{0}^2\\ \\ \\ \boxed{V=8}$