Integral
Lagt inn: 06/06-2017 17:28
Regn ut $\int_{0}^{2014} \int_{0}^{8} \frac{x^{2013}}{x^{2014}+8^{2014}} dxdy $
Matteprat
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https://www.matematikk.net/matteprat/viewtopic.php?f=19&t=45603
$ I=\int_{0}^{2014} \int_{0}^{8} \frac{x^{2013}}{x^{2014}+8^{2014}} dxdy $Eclipse skrev:Regn ut $\int_{0}^{2014} \int_{0}^{8} \frac{x^{2013}}{x^{2014}+8^{2014}} dxdy $
FintJanhaa skrev:$ I=\int_{0}^{2014} \int_{0}^{8} \frac{x^{2013}}{x^{2014}+8^{2014}} dxdy $Eclipse skrev:Regn ut $\int_{0}^{2014} \int_{0}^{8} \frac{x^{2013}}{x^{2014}+8^{2014}} dxdy $
[tex]u=x^{2014}+8^{2014}[/tex]
der
[tex]du=2014x^{2013}\,dx[/tex]
så
$ I=\frac{1}{2014}\int_{0}^{2014}\,dy \int_{8^{2014}}^{2*8^{2014}} \frac{du}{u} $
$ I=\frac{1}{2014}\int_{0}^{2014}\,dy \,\,\ln\left(\frac{2*8^{2014}}{8^{2014}}\right) $
[tex]I=\frac{2014}{2014}\,\ln(2) = \ln(2)[/tex]