Question

o valor da integral de 0 a 3 de -2 a 2 9x^2y^2 dydx é:

Answer 1

$\int\limits^3_0 {} \ \int\limits^2_{-2} {9x^2\cdot{y^2}} \, dy\ dx\\\\\\ \int\limits^3_0 {} \, 9x^2\cdot{ \dfrac{y^3}{3} }\bigg|_{-2}^2dx\\\\\\ \int\limits^3_0 {} \, \dfrac{9x^2\cdot(2)^3-9x^2\cdot(-2)^3}{3}dx\\\\\\ \dfrac{1}{3}\cdot{ \int\limits^3_0 {} \, [9x^2\cdot8-9x^2\cdot(-8)]dx }\\\\\\ \dfrac{1}{3}\cdot{ \int\limits^3_0 {} \, (72x^2+72x^2)dx }\\\\\\ \dfrac{144}{3}\cdot {\int\limits^3_0 {x^2} \, dx}\\\\\\ 48\codt{\bigg( \dfrac{x^3}{3}}\bigg)\bigg|_0^3\\\\\\16\cdot3^3= 432$

Answer 2

Resposta:

432 - Correto