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anonymous
 one year ago
Evaluate the integral using integration by parts w/ the indicated choices of u and dv
how do i do this? equation inside! thanks!!
anonymous
 one year ago
Evaluate the integral using integration by parts w/ the indicated choices of u and dv how do i do this? equation inside! thanks!!

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1442193899384:dw

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.2So the equation is: \[ \int\theta\cos(\theta)\,d\theta\\ u=\theta\\ dv=\cos(\theta)\,d\theta\\ \int u\,dv=uv\int v\,du \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes:) i'm a bit confused, so i find du and v, right? would du = ø and v = cosødø ?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Hmm if \(\large\rm u=\theta\) then \(\large\rm du\ne\theta\) You're taking a derivative with respect to theta :o \(\large\rm u'=1\) yes?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes :) ohh so du = 1 ?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2\[\large\rm \color{orangered}{u'}=1\]\[\large\rm \color{orangered}{\frac{du}{d\theta}}=1\qquad\to\qquad du=1\cdot d\theta\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh okay :) so which means du = dø ? and so would v be sinø ? :/

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2To get from \(\large\rm dv\) to \(\large\rm v\) you have to integrate. So going backwards from cosine gives us sine, ya that sounds right! :)\[\large\rm dv=\cos\theta~d\theta\qquad\to\qquad v=\sin\theta\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ooh yay!! :) and so now i do this?dw:1442194685139:dw

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2I wish you wouldn't use the "empty set" for your theta XD lol but ya looks good so far!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh haha oops :P it's just more convenient using that symbol instead of drawing it :P and so would it get sin2ø  (cosø)(ø) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0getting sin2ø + cos2ø + c ?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2In general: \(\large\rm a\cos(x)\ne\cos(ax)\) You can't just bring stuff inside of the trig function willy nilly like that.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh okay :( how do i do this part then? dw:1442195029862:dw

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2We leave this alone \(\large\rm \theta\sin\theta\) that will be part of our final answer

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2\[\large\rm \int\limits\sin\theta~d\theta\]Hmm looks like we made some kind of boo boo here on this integral.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2If you ignore the negative out front, what is the integral of sine?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Hmm, no we're going backwards. Going forwards, derivative of sine is cosine.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2\[\large\rm \color{orangered}{\int\limits\limits\sin\theta~d\theta}=\quad \color{orangered}{(\cos \theta+c)}\]Mmm ya that sounds better!

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2So you have:\[\large\rm \int\limits \theta \cos \theta~d \theta=\theta \sin \theta(\cos \theta+c)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh okay and so i simply it to øsinø + cos ø  c ?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Or even: \(\large\rm \theta\sin\theta+\cos\theta+C\) absorb the negative into the c, since it can represent any negative or positive value.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ahh okay! thank you!!:)
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