Question

O cálculo da Integral (foto) resulta em?

Answer 1

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Solução!

$\displaystyle{\int _{0} ^{5} } \frac{1}{ \sqrt[5]{x} }dx\\\\\\\\ \displaystyle{\int _{0} ^{5} } \frac{1}{x^{ \frac{1}{5} } }dx$


$\displaystyle{\int _{0} ^{5} } \frac{1. x^{ -\frac{1}{5}+1 } }{- \frac{1}{5}+1 }dx\\\\\\\\\\ \displaystyle{\int _{0} ^{5} } \frac{ x^{ \frac{4}{5} } }{ \frac{4}{5} }dx\\\\\\\\\\ \displaystyle{\int _{0} ^{5} } \frac{1}{ \sqrt[5]{x} } dx =\frac{5}{4} \sqrt[5]{ x^{4} }+c \\\\\\\\\ \bigg|_{0}^{5} =\frac{5}{4} \sqrt[5]{ 5^{4} }- \frac{5}{4} \sqrt[5]{ 0^{4} }\\\\\\\\ \bigg|_{0}^{5} =\frac{5}{4} \sqrt[5]{ 625 }-0\\\\\\\\ \bigg|_{0}^{5} =\frac{5}{4} \sqrt[5]{ 625}$



$\boxed{Resposta:\displaystyle{\int _{0} ^{5} } \frac{1}{ \sqrt[5]{x} } dx=\frac{5}{4} \sqrt[5]{ 625}}~~Alternativa~~A$

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Bons estudos!