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    Vector fields

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    Let a vector field F be given by
    F(x,y,z) = (x^3)i - (y^2)j + (2yz)k
    and a curve C be given by
    r(t) = 2ti + sintj - costk, 0 <= t <= (pi/2)

    1. Evaluate the line integral F*dr.
    2. Determine the arclength variable s from t.
    3. Determine the unit tangent vector T(s).
    4. Evaluate the total arclength L.
    5. Write the line integral in the from F(x(s), y(s), z(s)) * T(s) ds explicitly from L to 0.

    © BrainMass Inc. brainmass.com February 24, 2021, 2:34 pm ad1c9bdddf
    https://brainmass.com/math/vector-calculus/vector-fields-evaluating-integrals-29257

    Solution Preview

    See attachment

    Let a vector field F be given by
    F(x,y,z) = (x^3)i - (y^2)j + (2yz)k
    and a curve C be given by
    r(t) = 2ti + sintj - costk, 0 <= t <= (pi/2)

    1. ...

    Solution Summary

    This shows how to evaluate line integral, determine arclength variable, and determine unit tangent vector.

    $2.19

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