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Math Help - Math 264 Review

  1. #1
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    Math 264 Review

    Hi there, I just wandered in. I thought I had a fairly good idea of how to do #1, but I'm not too fond of the answer I keep finding. The problem in question is at the top of my scanned sheet dealing with work and line integral.
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  2. #2
    Behold, the power of SARDINES!
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    Note the vector field is conservative

    f(x,y,z)=\int2y^2zdx=2xy^2z+g(y,z)

    f_y(x,y,z)=4xyz+g_y(y,z)=4xyz

    so g can only be a function of z

    f_z(x,y,z)=2xy^2+g_z(z)=2xy^2+1 \iff g_z(z)=1 \iff g(z)=z

    so our function is

    f(x,y,z)=2xy^2z+z

    by the fundemental theorem of line integrals we can just evaluate at the end points for the value.

    r(0)=(1,0,0)
    r(\pi)=(-1,0,\frac{\pi}{6})

    f(-1,0,\pi/6)-f(1,0,0)=2(-1)(0)^2(\pi/6)+\pi/6-(2(1)(0)^2(0)-0)=\frac{\pi}{6}

    I hope this helps.
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  3. #3
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    It sure did. Thanks a bunch.
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