Calc. 3

Let C be the curve of intersection of the parabolic cylinder x2 = 2y, and the surface 3z = xy. Find the exact length of C from the origin to the point (4,8,32/3).

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  1. let x=t
    then y = t^2/2
    z = xy/3 = t^3/6

    then the arc length of the curve is

    ∫[0,4] √(1+t^2+t^4/4) dt = 44/3

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