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

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

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

TuringTest
 2 years ago
Best 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

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

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

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

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

TuringTest
 2 years ago
Best 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

husbishag
 2 years ago
Best 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?

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

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

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

TuringTest
 2 years ago
Best 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

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