Question

Seja uma integral tripla:
Assinale a alternativa correta quanto o valor da integral .

Answer 1

112/3 a resposta certa

Answer 2

Resposta:

Explicação passo-a-passo:

$\int\limits^2_0 \int\limits^2_0\int\limits^{x+2}_0  {2y} \, dy  \, dx \,dz\\\\Fica:\\\\\\\int\limits^2_0 \int\limits^2_0[\int\limits^{x+2}_0  {2y} \, dy ] \, dx \,dz\\\\\\\int\limits^2_0 \int\limits^2_0   \,\,\,   y^2|\limits^{x+2}_0 \, dx \,dz\\\\\\entao, \,y^2 - y^2 =  (x+2)^2 - 0^2 = x^2 + 4x + 4\\\\prosseguindo:\\\\\int\limits^2_0[ \int\limits^2_0 \, x^2 + 4x + 4\,dx ]\,dz\\\\\\\\\int\limits^2_0\,\,\,\frac{x^3}{3} + 2x^2 + 4x  \,\,\,|^2_0\\\frac{2^3}{3} + 2(2)^2 + 4(2) - 0  = 56/3.$

$\int\limits^2_0 {\frac{56}{3} } \, dz \\\\\\\\\frac{56}{3} \int\limits^2_0 {1} \, dz \\\\\\\frac{56}{3}( z)\\\\\\ substituindo \,os \,limiutes  \,\,|^2_0  = z-[z] = 2 -0 = 2\\\\logo\\\\\\\frac{56}{3}(2) = \frac{112}{3}$

Resposta alternativa (e)