O cálculo da Integral (foto) resulta em?
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![\displaystyle{\int _{0} ^{5} } \frac{1}{ \sqrt[5]{x} }dx\\\\\\\\
\displaystyle{\int _{0} ^{5} } \frac{1}{x^{ \frac{1}{5} } }dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Cint+_%7B0%7D+%5E%7B5%7D+%7D+%5Cfrac%7B1%7D%7B+%5Csqrt%5B5%5D%7Bx%7D+%7Ddx%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cdisplaystyle%7B%5Cint+_%7B0%7D+%5E%7B5%7D+%7D+%5Cfrac%7B1%7D%7Bx%5E%7B+%5Cfrac%7B1%7D%7B5%7D+%7D++%7Ddx "\displaystyle{\int _{0} ^{5} } \frac{1}{ \sqrt[5]{x} }dx\\\\\\\\
\displaystyle{\int _{0} ^{5} } \frac{1}{x^{ \frac{1}{5} } }dx")
![\displaystyle{\int _{0} ^{5} } \frac{1. x^{ -\frac{1}{5}+1 } }{- \frac{1}{5}+1 }dx\\\\\\\\\\ \displaystyle{\int _{0} ^{5} } \frac{ x^{ \frac{4}{5} } }{ \frac{4}{5} }dx\\\\\\\\\\ \displaystyle{\int _{0} ^{5} } \frac{1}{ \sqrt[5]{x} } dx =\frac{5}{4} \sqrt[5]{ x^{4} }+c \\\\\\\\\ \bigg|_{0}^{5} =\frac{5}{4} \sqrt[5]{ 5^{4} }- \frac{5}{4} \sqrt[5]{ 0^{4} }\\\\\\\\ \bigg|_{0}^{5} =\frac{5}{4} \sqrt[5]{ 625 }-0\\\\\\\\ \bigg|_{0}^{5} =\frac{5}{4} \sqrt[5]{ 625}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Cint+_%7B0%7D+%5E%7B5%7D+%7D+%5Cfrac%7B1.+x%5E%7B+-%5Cfrac%7B1%7D%7B5%7D%2B1+%7D+%7D%7B-+%5Cfrac%7B1%7D%7B5%7D%2B1+%7Ddx%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C+%5Cdisplaystyle%7B%5Cint+_%7B0%7D+%5E%7B5%7D+%7D+%5Cfrac%7B+x%5E%7B+%5Cfrac%7B4%7D%7B5%7D+%7D+%7D%7B+%5Cfrac%7B4%7D%7B5%7D+%7Ddx%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C+%5Cdisplaystyle%7B%5Cint+_%7B0%7D+%5E%7B5%7D+%7D+%5Cfrac%7B1%7D%7B+%5Csqrt%5B5%5D%7Bx%7D+%7D+dx+%3D%5Cfrac%7B5%7D%7B4%7D+%5Csqrt%5B5%5D%7B+x%5E%7B4%7D+%7D%2Bc+%5C%5C%5C%5C%5C%5C%5C%5C%5C+%5Cbigg%7C_%7B0%7D%5E%7B5%7D+%3D%5Cfrac%7B5%7D%7B4%7D+%5Csqrt%5B5%5D%7B+5%5E%7B4%7D+%7D-+%5Cfrac%7B5%7D%7B4%7D+%5Csqrt%5B5%5D%7B+0%5E%7B4%7D+%7D%5C%5C%5C%5C%5C%5C%5C%5C+%5Cbigg%7C_%7B0%7D%5E%7B5%7D+%3D%5Cfrac%7B5%7D%7B4%7D+%5Csqrt%5B5%5D%7B+625+%7D-0%5C%5C%5C%5C%5C%5C%5C%5C+%5Cbigg%7C_%7B0%7D%5E%7B5%7D+%3D%5Cfrac%7B5%7D%7B4%7D+%5Csqrt%5B5%5D%7B+625%7D "\displaystyle{\int _{0} ^{5} } \frac{1. x^{ -\frac{1}{5}+1 } }{- \frac{1}{5}+1 }dx\\\\\\\\\\ \displaystyle{\int _{0} ^{5} } \frac{ x^{ \frac{4}{5} } }{ \frac{4}{5} }dx\\\\\\\\\\ \displaystyle{\int _{0} ^{5} } \frac{1}{ \sqrt[5]{x} } dx =\frac{5}{4} \sqrt[5]{ x^{4} }+c \\\\\\\\\ \bigg|_{0}^{5} =\frac{5}{4} \sqrt[5]{ 5^{4} }- \frac{5}{4} \sqrt[5]{ 0^{4} }\\\\\\\\ \bigg|_{0}^{5} =\frac{5}{4} \sqrt[5]{ 625 }-0\\\\\\\\ \bigg|_{0}^{5} =\frac{5}{4} \sqrt[5]{ 625}")
![\boxed{Resposta:\displaystyle{\int _{0} ^{5} } \frac{1}{ \sqrt[5]{x} } dx=\frac{5}{4} \sqrt[5]{ 625}}~~Alternativa~~A](https://tex.z-dn.net/?f=%5Cboxed%7BResposta%3A%5Cdisplaystyle%7B%5Cint+_%7B0%7D+%5E%7B5%7D+%7D+%5Cfrac%7B1%7D%7B+%5Csqrt%5B5%5D%7Bx%7D+%7D+dx%3D%5Cfrac%7B5%7D%7B4%7D+%5Csqrt%5B5%5D%7B+625%7D%7D%7E%7EAlternativa%7E%7EA "\boxed{Resposta:\displaystyle{\int _{0} ^{5} } \frac{1}{ \sqrt[5]{x} } dx=\frac{5}{4} \sqrt[5]{ 625}}~~Alternativa~~A")
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Solução!
Boa tarde!
Bons estudos!
Usuário anônimo:
A alternativa c que esta marcada esta errada.
Perfeito, muito obrigado!
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