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    I must integrate \int_C \vec{F} \cdot d\vec{r}

    where C is given by parametric equations x = t^4, y = 0, z = t^2 and \vec{F} = xz\hat{i} +z^2 \hat{j} + x^2 \hat{k}

    Haven't got a clue
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      What's your definition of a line integral?
      Also, where does t vary between?
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      (Original post by Glutamic Acid)
      What's your definition of a line integral?
      Also, where does t vary between?
      Well since the vector field isn't conservative, I'm not sure.

      What t varies between can only be seen from the fact the line integral is between (0, 0, 0) and (1, 0, 1) which I forgot to mention for some reason
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      This is some of my working:

      \frac{dr}{dt} = <3t^2, 0, 1>

      Thus \int _C \vec{F} . d \vec{r} = \int _C <xy, z^2, x^2> . <3t^2, 0, 1> dt

      Is this near right?
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      Anyone understand where I'm going wrong?
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      (Original post by Dagnabbit)
      This is some of my working:

      \frac{dr}{dt} = <3t^2, 0, 1>

      Thus \int _C \vec{F} . d \vec{r} = \int _C <xy, z^2, x^2> . <3t^2, 0, 1> dt

      Is this near right?
      You said "C is given by parametric equations x = t^4, y = 0, z = t^2" so I'd check this bit <3t^2, 0, 1> if I were you.

      Once you've done that, express x, y and z in terms of t, do the dot product and integrate between your limits.
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