Question

Qual é a integral definida de

Answer 1

$\displaystyle \int\limits^{\pi}_0\text{cos x dx} \\\\\\ -\int\limits^{\pi}_0-\text{cos x dx} \\\\\\ -[\ \text{sen }\pi -\text{sen 0}\ ] \\\\\\ -[\ 0-0 \ ] \\\\\\ \huge\boxed{\ 0\ }\checkmark$

letra d

Answer 2

✅ Após resolver os cálculos, concluímos que o a integral definida da procurada da função em foco é:

    $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf \int_{0}^{\pi} \cos x\,dx = 0\:\:\:}}\end{gathered} }$

Portanto, a opção correta é:

           $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf Letra\: D\:\:\:}}\end{gathered} }$

   

Seja a integral definida:

             $\Large\displaystyle\begin{gathered}\tt \int_{0}^{\pi} \cos x\,dx\end{gathered}$

Nesta situação, a função que desejamos integrá-la é:

             $\Large\displaystyle\begin{gathered}\tt f(x) = \cos x\end{gathered}$  

Calculando a referida integral, temos:

    $\Large\displaystyle\begin{gathered}\tt \int_{0}^{\pi} \cos x\,dx = (\sin x + c)|_{0}^{\pi}\end{gathered}$

                               $\Large\displaystyle\begin{gathered}\tt = (\sin \pi + c) - (\sin 0 + c)\end{gathered}$

                               $\Large\displaystyle\begin{gathered}\tt = \sin \pi + c - \sin 0 - c\end{gathered}$

                               $\Large\displaystyle\begin{gathered}\tt = \sin \pi - \sin 0\end{gathered}$

                               $\Large\displaystyle\begin{gathered}\tt = 0 - 0\end{gathered}$

                               $\Large\displaystyle\begin{gathered}\tt = 0\end{gathered}$

Portanto, a integral definida procurada é:

     $\Large\displaystyle\begin{gathered}\tt \int_{0}^{\pi} \cos x\,dx = 0\end{gathered}$

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Veja a solução gráfica da questão representada na figura: