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| Author | Message / Information |
| SonofBohr Quote | Reply | | Antiderivative of e^x/2 posted on: 10/25/2006 6:04:48 PM Antiderivative of e^x/2 I believe the anwser is 2e^x/2 but what formula was used to get this? Thanks |
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Anomalies
Quote | Reply | This message was updated on 10/27/2006 7:40:16 AM by Anomalies |
Antiderivative of e^x/2
replied on: 10/27/2006 7:39:29 AM Just think about what function gives you e^x/2 when differentiated. One way is consider how to differentiate e^ax d/dx exp(ax) = a exp(ax) so integrate this exp(ax) = \int a exp(ax) dx Thus \int exp(ax) dx = a^{-1} exp(a x) which gives your answer with a = 1/2 However, we have missed out a possible constant. |
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Grogler
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Antiderivative of e^x/2
replied on: 11/8/2006 8:30:04 AM There is no any formulas when you calculate integrals (except table of integrals, which you can simply find in the Inet). It is more difficult to calculate integrals than calculate derivatives, as we can even teach monkey for derivatives, however finding integrals sometimes equating to the ART... So I think it is better not to use formulas for integrals. If you will guess the solutions, then, during some time, this formulas will occur by themselves... |
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minase
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Antiderivative of e^x/2
replied on: 12/11/2007 8:42:02 PM Substitution... u=x/2 du=1/2dx /int e^(x/2)dx=/int2(e^u)du =2/int(e^u)du <<=constant out =2e^u+c =2e^(x/2)+c |
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