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    Vector Integrals : Stokes' Theorem and Line Integral of a Vector Field

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    7.. Given the vector field F(x,y,z) = xi + (x+2y+3z) j + z2 k
    Let C he the circle on the xy-plane, centered at the origin (0,0) and having as radius r=5. Let S be the part of the paraboloid z = 16? x2 ? y2 which lies above the xy-plane (z ≤ 0). Use the Stokes's Theorem to evaluate the line integral of this vector field along C.

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    The line integral of a vector field is calculated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.