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Math Help - For the vector field F(x,y,z) =

  1. #1
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    For the vector field F(x,y,z) =

    For the vector field
    F(x,y,z) = e^y i + xe^y j + (z+1)e^z k, where


    C: r(t) = t i + t^2 j + t^3 k, 0 ≤ t ≤1


    Find a function such that F = grad


    and use the above to evaluate ∫C Fdr along C
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  2. #2
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    Can you prove that F is a conservative field?
    Vector fields that are conservative have integrals that are path independent.
    Can you show that \phi  = xe^y  + ze^z \quad  \Rightarrow \quad \nabla \phi  = F?
    What is \phi (1) - \phi (0)?
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