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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

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  1. myko
    • 2 years ago
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    make variable change to cyulindrical coordinates first with r=2

  2. myko
    • 2 years ago
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    x=2cost y=2sint z=z so: dx=-2sint*dt dy=2cost*dt dz=dz

  3. meggiesmermaid
    • 2 years ago
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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

  4. TuringTest
    • 2 years ago
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    t is bound above by 2 or 2pi?

  5. TuringTest
    • 2 years ago
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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)

  6. meggiesmermaid
    • 2 years ago
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    \[0\le t \le 2\pi\]

  7. TuringTest
    • 2 years ago
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    that makes more sense obviously so did you try it yet?

  8. meggiesmermaid
    • 2 years ago
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    no the homework is not due till tonight so im studying for my test and will try it after!

  9. TuringTest
    • 2 years ago
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    good luck!

  10. meggiesmermaid
    • 2 years ago
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    i got 3 pi but it was incorrect.

  11. TuringTest
    • 2 years ago
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    \[\int_0^{2\pi}-2t\sin t+4\cos^2t+4\sin t\cos tdt\]\[2t\cos t-2\sin t+2t+\sin(2t)+2\sin t|_0^{2\pi}\]is that what you got?

  12. meggiesmermaid
    • 2 years ago
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    no my signs were messed up.

  13. TuringTest
    • 2 years ago
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    let me check with wolfram...

  14. meggiesmermaid
    • 2 years ago
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    thats correct! i finished it!

  15. meggiesmermaid
    • 2 years ago
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    i had too many subtraction signs.

  16. TuringTest
    • 2 years ago
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    cool :) yeah, the algebra can be the worst in calc 3

  17. meggiesmermaid
    • 2 years ago
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    hahhaa. yeah. thanks so much. :)

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