anonymous
  • anonymous
Evaluate the line integral zdx+xdy+xydz where is the path of the helix r(t)=(2cost)i+(2sint)j+(1t)k on 0 less than t less than 2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
make variable change to cyulindrical coordinates first with r=2
anonymous
  • anonymous
x=2cost y=2sint z=z so: dx=-2sint*dt dy=2cost*dt dz=dz
anonymous
  • anonymous
i got to \[\int\limits_{0}^{2\pi} -2 tsintdt +4\cos^2tdt + 4costsintdt\] but i cant figure put how to integrate

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TuringTest
  • TuringTest
t is bound above by 2 or 2pi?
TuringTest
  • TuringTest
first term: integrate by parts second term: double angle formula \(\cos^2t=\frac12(1+\cos(2t))\) third term: u=sin(t)
anonymous
  • anonymous
\[0\le t \le 2\pi\]
TuringTest
  • TuringTest
that makes more sense obviously so did you try it yet?
anonymous
  • anonymous
no the homework is not due till tonight so im studying for my test and will try it after!
TuringTest
  • TuringTest
good luck!
anonymous
  • anonymous
i got 3 pi but it was incorrect.
TuringTest
  • TuringTest
\[\int_0^{2\pi}-2t\sin t+4\cos^2t+4\sin t\cos tdt\]\[2t\cos t-2\sin t+2t+\sin(2t)+2\sin t|_0^{2\pi}\]is that what you got?
anonymous
  • anonymous
no my signs were messed up.
TuringTest
  • TuringTest
let me check with wolfram...
anonymous
  • anonymous
thats correct! i finished it!
anonymous
  • anonymous
i had too many subtraction signs.
TuringTest
  • TuringTest
cool :) yeah, the algebra can be the worst in calc 3
anonymous
  • anonymous
hahhaa. yeah. thanks so much. :)

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