Question

O valor da integral da figura. Escolha uma: a. 1/6 b. 1/8 c. 1/5 d. 1/4 e. 1/7

Answer 1

Boa tarde Aline!

Solução!

$\displaystyle\int_{0}^{1} }\bigg[ \displaystyle\int_{ x^{2} }^{x} dy}\bigg]dx\\\\\\\\\ \displaystyle\int_{0}^{1} } (x- x^{2})dx\\\\\\\\ I=\bigg[ \dfrac{ x^{2} }{2}- \dfrac{ x^{3} }{3}\bigg]_{0}^{1}\\\\\\\ I=\bigg( \dfrac{ x^{2} }{2}- \frac{ x^{3} }{3}\bigg)-\bigg( \dfrac{ x^{2} }{2}- \dfrac{ x^{3} }{3}\bigg)\\\\\\\ I=\bigg( \dfrac{ 1^{2} }{2}- \dfrac{ 1^{3} }{3}\bigg)-\bigg( \dfrac{ 0^{2} }{2}- \dfrac{ 0^{3} }{3}\bigg)\\\\\\\ I=\bigg( \dfrac{ 1 }{2}- \frac{ 1 }{3}\bigg)$


$I=\bigg( \dfrac{ 3-2 }{6}\bigg)\\\\\\ I= \dfrac{1}{6}\\\\\\\ \boxed{Resposta:~~I= \dfrac{1}{6}~~\boxed{Alternativa~~A}}$

Boa tarde!
Bons estudos!

Answer 2

Resposta:

1/6 Correto

Explicação passo a passo: