Question

o calculo da integral dx/raiz quinta se x no limite de zero a 5

Answer 1

$F_{(x)} = \displaystyle \int_{0}^{5} \dfrac{dx}{\sqrt[5]{x}}\\\\ F_{(x)} = \displaystyle \int_{0}^{5} x^{-\frac{1}{5}} .dx\\\\\\ Integrando:\\\\ \displaystyle \int_{0}^{5} \dfrac{dx}{\sqrt[5]{x}} = \left \dfrac{x^{-\frac{1}{5}+1}}{-\frac{1}{5}+1} \right |_{0}^{5}$


$\displaystyle \int_{0}^{5} \dfrac{dx}{\sqrt[5]{x}} = \left \dfrac{x^{\frac{4}{5}}}{\frac{4}{5}} \right |_{0}^{5}\\\\\\ \displaystyle \int_{0}^{5} \dfrac{dx}{\sqrt[5]{x}} = \left \dfrac{5\sqrt[5]{x^4}}{4} \right |_{0}^{5}\\\\\\ \displaystyle \int_{0}^{5} \dfrac{dx}{\sqrt[5]{x}} = \dfrac{5\sqrt[5]{5^4}}{4} - \dfrac{5\sqrt[5]{0^4}}{4}$


$\displaystyle \int_{0}^{5} \dfrac{dx}{\sqrt[5]{x}} \approx \dfrac{18,1194916}{4} - 0\\\\\\ \boxed{\displaystyle \int_{0}^{5} \dfrac{dx}{\sqrt[5]{x}} \approx 4,52987}$



Espero ter ajudado.
Bons estudos!