meggiesmermaid
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



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myko
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make variable change to cyulindrical coordinates first with r=2

myko
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x=2cost
y=2sint
z=z
so:
dx=2sint*dt
dy=2cost*dt
dz=dz

meggiesmermaid
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i got to \[\int\limits_{0}^{2\pi} 2 tsintdt +4\cos^2tdt + 4costsintdt\] but i cant figure put how to integrate

TuringTest
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t is bound above by 2 or 2pi?

TuringTest
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first term: integrate by parts
second term: double angle formula \(\cos^2t=\frac12(1+\cos(2t))\)
third term: u=sin(t)

meggiesmermaid
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\[0\le t \le 2\pi\]

TuringTest
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that makes more sense obviously
so did you try it yet?

meggiesmermaid
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no the homework is not due till tonight so im studying for my test and will try it after!

TuringTest
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good luck!

meggiesmermaid
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i got 3 pi but it was incorrect.

TuringTest
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\[\int_0^{2\pi}2t\sin t+4\cos^2t+4\sin t\cos tdt\]\[2t\cos t2\sin t+2t+\sin(2t)+2\sin t_0^{2\pi}\]is that what you got?

meggiesmermaid
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no my signs were messed up.

TuringTest
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let me check with wolfram...

meggiesmermaid
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thats correct!
i finished it!

meggiesmermaid
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i had too many subtraction signs.

TuringTest
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cool :) yeah, the algebra can be the worst in calc 3

meggiesmermaid
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hahhaa. yeah. thanks so much. :)