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

Question

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

anonymous · Answer

make variable change to cyulindrical coordinates first with r=2

anonymous · Answer

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

anonymous · Answer

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

turingtest · Answer

t is bound above by 2 or 2pi?

turingtest · Answer

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

anonymous · Answer

$$0\le t \le 2\pi$$

turingtest · Answer

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

anonymous · Answer

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

turingtest · Answer

good luck!

anonymous · Answer

i got 3 pi but it was incorrect.

turingtest · Answer

$$\int_0^{2\pi}-2t\sin t+4\cos^2t+4\sin t\cos tdt$$$$2t\cos t-2\sin t+2t+\sin(2t)+2\sin t|_0^{2\pi}$$is that what you got?

anonymous · Answer

no my signs were messed up.

turingtest · Answer

let me check with wolfram...

anonymous · Answer

thats correct! 
i finished it!

anonymous · Answer

i had too many subtraction signs.

turingtest · Answer

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

anonymous · Answer

hahhaa. yeah. thanks so much. :)