Question

A integral ∫ x³ dx vale :

A) $\frac{ x^{4} }{4} + c$

B) $\frac{ x^{3} }{3} + c$

C) $\frac{ x^{3} }{3} + c$

D) x + c

E) 3 x² + c

Answer 1

Resolução da questão, veja:

Alternativa “A” é a correta:

Para resolver isso vamos utilizar a seguinte propriedade:

$\Large\boxed{\boxed{\boxed{\boxed{\mathbf{\displaystyle\int(t^{n})~dt=\dfrac{t^{n+1}}{n+1}}+\mathbf{C}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

Observe:

$\mathsf{\displaystyle\int~x^{3}~dx}}}}}}}\\\\\\\\\\ \mathsf{\dfrac{x^{3+1}}{3+1}}}+\mathsf{C}}}\\\\\\\\\\ \Large\boxed{\boxed{\boxed{\boxed{\boxed{\mathbf{~\therefore~\displaystyle\int{x^{3}~dx=\dfrac{x^{4}}{4}}+\mathbf{C}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}~\checkmark$

Espero que te ajude. '-'