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Thread: Integral of Line

  1. #1
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    Integral of Line

    What is integral of line ?
    How do I calculate?

    Example: C is segment of straight of (0,0) until (0,1). How do I calculate:

    $\displaystyle \int_C senxy dy$

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  2. #2
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    Quote Originally Posted by Apprentice123 View Post
    What is integral of line ?






    How do I calculate?



    Example: C is segment of straight of (0,0) until (0,1). How do I calculate:



    $\displaystyle \int_C senxy dy $










    What is "sen" ?
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  3. #3
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    Sory in english $\displaystyle sin$
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  4. #4
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    Just substitute x=0 (y from 0 to 1) into the integral and integrate along the y axis.
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  5. #5
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    The answer this integral is 0 ?

    And the intregral line

    $\displaystyle \int_C 3x^2yzds$
    $\displaystyle C: x = t, y = t^2, z = \frac{2}{3}z^3$
    $\displaystyle 0 \leq t \leq 1$

    The answer is $\displaystyle \frac{197}{180}$ ???
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  6. #6
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    Quote Originally Posted by Apprentice123 View Post
    The answer this integral is 0 ?

    And the intregral line

    $\displaystyle \int_C 3x^2yzds$
    $\displaystyle C: x = t, y = t^2, z = \frac{2}{3}z^3$
    $\displaystyle 0 \leq t \leq 1$

    The answer is $\displaystyle \frac{197}{180}$ ???
    $\displaystyle z = \frac{2}{3}t^3$ ?
    I think the answer is $\displaystyle \frac{13}{20}$
    Last edited by curvature; Apr 25th 2009 at 06:57 AM.
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  7. #7
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    The first integral $\displaystyle \int_C sinxy dy$ the answer is 0 ?

    And the other integral where you resolved ?
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  8. #8
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    [quote=Apprentice123;304717]The first integral $\displaystyle \int_C sinxy dy$ the answer is 0 ? quote]

    Yes. Because sinxy=0 on the line x=0.
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  9. #9
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    In
    $\displaystyle \int_C 3x^2yzds$
    $\displaystyle C: x = t, y = t^2, z = \frac{2}{3}t^3$
    $\displaystyle 0 \leq t \leq 1$

    how you found $\displaystyle \frac{13}{20}$ ?
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