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Math Help - Line Integral.

  1. #1
    Super Member Showcase_22's Avatar
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    Line Integral.

    Evaluate \int_C(xy+y+z)~ds along the curve \underline{r}(t)=2ti+tj+(2-2t)k where 0 \leq t \leq 1.
    \left| \underline{v} \right|= \left| \frac{d \underline{r}}{dt} \right|=\left| 2i+j-2k \right|=3

    \int_0^1 2t^2+t+2-2t ~dt=\int_0^1 2t^2-t+2 ~dt= \left[ \frac{2t^3}{3}-\frac{t^2}{2}+2t \right]_0^1=\frac{2}{3}-\frac{1}{2}+2=\frac{13}{6}

    Is this right?
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  2. #2
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    Hi

    You have forgotten to multiply by \left| \underline{v} \right|= 3
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  3. #3
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    The correct is
    \int_0^1 (6t^2-3t+6)dt

    ???
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  4. #4
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    Quote Originally Posted by Apprentice123 View Post
    The correct is
    \int_0^1 (6t^2-3t+6)dt

    ???
    Yes.
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  5. #5
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    Thank you.
    Can I post my problem and the solution to see if it is correct in a new topic ?
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  6. #6
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    Quote Originally Posted by Apprentice123 View Post
    Thank you.
    Can I post my problem and the solution to see if it is correct in a new topic ?
    Yes. Post it in a new thread.
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