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husbishag
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Compute ∫ x cos(x)dx.
Would we use Integration by Parts and compute this as  sin(x) = Cos(x) + C ????
 2 years ago
 2 years ago
husbishag Group Title
Compute ∫ x cos(x)dx. Would we use Integration by Parts and compute this as  sin(x) = Cos(x) + C ????
 2 years ago
 2 years ago

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husbishag Group TitleBest ResponseYou've already chosen the best response.0
I wrote that incorrectly. sin(x)+ cos(x) + C
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
close, but not quite
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
\[u=x\]\[dv=\cos xdx\]\[\int udv=uv\int vdu\]look carefully and you should be able to see you dropped an x in there
 2 years ago

husbishag Group TitleBest ResponseYou've already chosen the best response.0
@TuringTest , I'm a little confused on your explanation, where have I dropped an x?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
u=x, and there is a u on the right of the formula. There should be an x where the u is...
 2 years ago

husbishag Group TitleBest ResponseYou've already chosen the best response.0
@TuringTest I think I see. So, it would be sin(x) + x cos(x) + C
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
what you have above is\[vdu\int uv\]careful, identify your v and u, dv and du!
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
\[u=x\implies du=dx\]\[dv=\cos xdx\implies v=\sin x\]\[\int udv=uv\int vdu\]slowly and carefully plug in each for u, v, and du
 2 years ago

husbishag Group TitleBest ResponseYou've already chosen the best response.0
@TuringTest Thank you for your patience with me. Would it be x sin x + cos x + C?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
\[u=x\implies du=dx\]\[dv=\cos xdx\implies v=\sin x\]\[\int udv=uv\int vdu\]\[\int x\cos xdx=x(\sin x)\int(\sin x)dx=x\sin x+\int\sin xdx\]
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
crap I made up a negative sign
 2 years ago

RadEn Group TitleBest ResponseYou've already chosen the best response.1
int cosx = sinx not sinx
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
\[u=x\implies du=dx\]\[dv=\cos xdx\implies v=\sin x\]\[\int udv=uv\int vdu\]\[\int x\cos xdx=x(\sin x)\int(\sin x)dx=x\sin x+\int\sin xdx\]yeah you were right, my bad :P
 2 years ago

husbishag Group TitleBest ResponseYou've already chosen the best response.0
If only one day I could understand math that way both of you do... thanks for your help!
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
welcome!
 2 years ago
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