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Homework Help: Setting up parametrization

  1. Dec 1, 2011 #1
    1. The problem statement, all variables and given/known data
    Compute the line integral of the scalar function.
    f(x,y,z) = x[itex]e^{z^2}[/itex], piecewise linear path from (0,0,1) to (0,2,0) to (1,1,1)

    2. Relevant equations



    3. The attempt at a solution
    In this problem, all I need is a parametrization. First I drew the line from (0,0,1) to (0,2,0) xyz-plane. I got the slope as z = 1 - [itex]\frac{y}{2}[/itex]. So I set y = t then z will be 1 - [itex]\frac{t}{2}[/itex]. I got parametrization as c(t) = <0,t,1-[itex]\frac{y}{2}[/itex]>. But it's wrong. It's c(t) = <0,2t,1-2t>. Would anyone help me how to get parametrization ??
     
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  3. Dec 2, 2011 #2

    HallsofIvy

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    Science Advisor

    Yes, the line from (0, 0, 1) to (0, 2, 0) can be written as z= 1- y/2. Since you are using t as parameter, that would be <0, t, 1- t/2>. Why do you say that is wrong?
    When t= 0, your parameterization gives (0, 0, 1) and when t= 2, it gives (0, 2, 1). A line is determined by two points so it gives the correct line.

    It is c(t)= <0, 2t, 1- 2t> that is wrong. In order that y= 2t= 2, t must be 1. But then z= 1- 2= -1, not 0.
     
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