anonymous
  • anonymous
integrate 2t x csc^2t dt
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\int\limits_{}^{} 2\Theta \csc ^{2}\Theta \]
zepdrix
  • zepdrix
`Integration by Parts` \:)/ Do you remember the anti-derivative of csc^2x or maybe -csc^2x?
anonymous
  • anonymous
Looking in my notes

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anonymous
  • anonymous
-cotx
anonymous
  • anonymous
ohhhh, so this is a straightforward integration by parts problem?
anonymous
  • anonymous
no crazy trickery?
zepdrix
  • zepdrix
Yah it doesn't look like there is anything sneaky going on here :)
zepdrix
  • zepdrix
Oh I guess we'll have to deal with the integral of cotx, which you may or may not have in your notes. That is rather tricky to get through if it's not in your notes :D
zepdrix
  • zepdrix
Oh wait wait, I was confusing \(\large \int \csc\theta\) with \(\large \cot\theta\). Cotangent shouldn't be too bad actually. :D Convert to sines and cosines and do a u-sub. Lemme know if you get stuck anywhere.
anonymous
  • anonymous
umm, I got \[-2Thetacot \Theta+\ln \left| sinx \right|\]
zepdrix
  • zepdrix
Only one minor problem. Your \(\large u=2\theta\), so your \(\large du=2\) So your integral that involved cot theta should have a 2 in front of it. And also try to keep everything the same variable :) lol I see theta's and x's in your solution. I make that mistake sometimes myself.
anonymous
  • anonymous
I still have the answer wrong :(
zepdrix
  • zepdrix
\[\Large -2\theta \cot \theta+\color{royalblue}{2}\ln|\sin \theta|+C\] Understand where the blue 2 is coming from? :o
anonymous
  • anonymous
wait, no, I got it. Cool. Thank you!
anonymous
  • anonymous
I understand what I was doing wrong.

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