Question

Escolha um dos dois temas seguintes, relativos à questão racial no ... da integral ∫_0^1 6x^2(x^3+2)^2 dx é? a. 38/3 b. 12 c. 6 d. 0 e. 1/13.

Answer 1

$\int\limits^1_0 {6x^2.(x^3+2)^2} \, dx\\\\ u = x^3+2\\u'=3x^2dx\\\\ =\int\limits { \dfrac{6u^2}{3} } \, du\\\\ =\int\limits {2u^2} \, du\\\\ = \dfrac{2u^3}{3}\\\\ \int\limits^1_0 {6x^2.(x^3+2)^2} \, dx =\dfrac{2(x^3+2)^3}{3}\bigg|_0^1\\\\=2.\dfrac{3^3}{3}-2.\dfrac{2^3}{3}\\\\= \dfrac{54-16}{3} \\\\\boxed{=\dfrac{38}{3}}}$