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jennychan12
 2 years ago
integral from 0 to 1 of [e^x(cos(e^x))]dx ?
jennychan12
 2 years ago
integral from 0 to 1 of [e^x(cos(e^x))]dx ?

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jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{1} [e^x \cos (e^x)]dx\]

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.2Do a usubstitution with \(u=\sin(e^x)\), and your solution should pop right out.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0but if you do that, then du = e^xcos(e^x) and there's no cos (e^x) in the question.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0that'd just be ucosu

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.2\(u=\sin(e^x)\implies du=e^x\cos(e^x)dx\). So your integral becomes\[\int du=u\]

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.2Substitute back for \(u\), and you get \[\int_0^1 e^x\cos(e^x)dx=\sin(e^x)_0^1\]

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1u =e^x du = e^x dx \(\int cos udu\) ohh..now i could say that u =sin e^x is a better substitution..

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0oh wait. my bad. i thought u said u = sin u ok i see now

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.2Yup, I like to call my method "guessing the solution and proving you're right"

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.2Although if you really had no clue of the solution, \(u=e^x\) would be a fine substitution. You would just have to integrate by parts.

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1whenever i see a nonstandard angle with sin/cos/.. i'll call that as 'bad angle' and put u= bad angle.... example : sin x^2 , cos log x ....

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1how do we need integration by parts ?? O.o u= e^x du=e^xdx

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.2Oh. Right. You don't. Ignore my ramblings.
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