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Bestem det uegentlige integralet
Posted: 31/10-2006 00:25
by monster
Bestem det uegentlige integralet til
Bestem denne integralen
Posted: 31/10-2006 03:07
by daofeishi
[tex]\int _0 ^\infty 2e^{-x} dx = 2[-e^{-x}]_0 ^\infty = 2[0 - (-1)] = 2[/tex]
[tex] \int _0 ^{\sqrt[3]{\pi}} x^2 \cos (x^3) dx = \int _0 ^{\sqrt[3]{\pi}} \cos(u) \frac{1}{3}\frac{du}{dx} dx = \frac{1}{3}[\sin (x^3)]_0 ^{\sqrt[3]{\pi}} = \frac{1}{3}[0-0] = 0[/tex]
Posted: 31/10-2006 13:32
by monster
[tex]\int _0 ^\2 (\frac{1}{x^2} + \frac{1}{x}) dx[/tex]
blir den [tex]lnx^2 + lnx [/tex] oxo setter vi 2 og null inn osv.?
Posted: 31/10-2006 15:14
by monster
hva bruker vi for å løse denne?
Posted: 31/10-2006 15:26
by Janhaa
monster wrote:[tex]\int _0 ^\2 (\frac{1}{x^2} + \frac{1}{x}) dx[/tex]
blir den [tex]lnx^2 + lnx [/tex] oxo setter vi 2 og null inn osv.?
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[tex]\int ({1\over x^2}\;+\;{1\over x})dx[/tex]
Husk at:
[tex]\int ({1\over x^2})dx\;=\;[/tex][tex]{-1\over x}\;+\;C[/tex]
[tex]\int ({1\over x^2}\;+\;{1\over x})dx\;=\;[/tex][tex]{-1\over x}\;+\;ln(x)\;+\;C[/tex]