## meggiesmermaid 2 years ago 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

1. myko

make variable change to cyulindrical coordinates first with r=2

2. myko

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

3. meggiesmermaid

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

4. TuringTest

t is bound above by 2 or 2pi?

5. TuringTest

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

6. meggiesmermaid

$0\le t \le 2\pi$

7. TuringTest

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

8. meggiesmermaid

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

9. TuringTest

good luck!

10. meggiesmermaid

i got 3 pi but it was incorrect.

11. 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?

12. meggiesmermaid

no my signs were messed up.

13. TuringTest

let me check with wolfram...

14. meggiesmermaid

thats correct! i finished it!

15. meggiesmermaid

i had too many subtraction signs.

16. TuringTest

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

17. meggiesmermaid

hahhaa. yeah. thanks so much. :)