Question

Qual a primitiva da função f(x)=-1/2x²?

Answer 1

Ola Khaayan

f(x) = -x²/2 

primitiva
F(x) = -x³/6 + C

Answer 2

✅ Após resolver os cálculos, concluímos que a primitiva da referida função é:

  $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf \int \bigg(-\frac{1}{2}\bigg)x^{2}\,dx = -\frac{1}{6}x^{3},\:\:\:\:c\in\mathbb{R}\:\:\:}}\end{gathered} }$

Seja a função polinomial:

           $\Large\displaystyle\begin{gathered}\tt f(x) = \bigg(-\frac{1}{2}\bigg)x^{2}\end{gathered}$

Para calcular a primitiva de uma função devemos prestar atenção na seguinte propriedade:

            $\Large\displaystyle\text{ \begin{gathered}\tt \int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}\end{gathered} }$

Então, temos:

   $\Large\displaystyle\text{ \begin{gathered}\tt \int \bigg(-\frac{1}{2}\bigg)x^{2}\,dx = -\frac{1}{2}\cdot\frac{x^{2 + 1}}{2 + 1} + c\end{gathered} }$

                                       $\Large\displaystyle\begin{gathered}\tt = -\frac{1}{2}\cdot\frac{1}{3}\cdot x^{3}+ c\end{gathered}$

                                       $\Large\displaystyle\begin{gathered}\tt = -\frac{1}{6}x^{3} + c\end{gathered}$

   

✅ Portanto, a primitiva procurada é:

     $\Large\displaystyle\begin{gathered}\tt \int \bigg(\frac{1}{2}\bigg)x^{2}\,dx = -\frac{1}{6}x^{3}\end{gathered}$

$\LARGE\displaystyle\text{ \begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered} }$

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$\Large\displaystyle\text{ \begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Observe \:o\:Gr\acute{a}fico!!\:\:\:}}}\end{gathered} }$