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    Integrals, moment of inertia, and Stokes theorem

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    1
    Evaluate
    3∫1
    1-∫-2
    (x2y-2xy3)dydx

    2
    Correctly reverse the order of integration, then evaluate
    1∫0
    1∫y
    xeydxdy

    3
    The plane region R is bounded by the graphs of y=x and y=x2 .
    Find the volume over R and beneath the graph of f(x, y) = x + y.

    4
    Find the volume of the "ice cream cone" bounded by the sphere x2+y2+z2=1 and the cone
    z
    =
    ^/¯x2+y2-1

    5
    Find the moment of inertia around the z-axis of the solid bounded by
    x = 0, y = 0, z = 0, y = 1 - x2, and 4x + 3y + 2z = 12, assume _(x,y,z)_1.
    6
    Evaluate ∫CP(x,y)dx+Q(x,y)dy
    Given: P(x,y)=y2, Q(x,y)= 3x; C is the part of the graph of y=3x2 from (-1,3) to (2,12).

    7
    Use the divergence theorem to evaluate
    ∫∫s F?nds where n is the outer unit normal vector to the surface S. ∫∫F = 3xi + 2y2j + 4zk;
    S is the surface of the plane x + y + z = 6.
    8
    Use Stokes theorem to evaluate W = F?Tds where F(x, y, z) = 3yi - 2xj +4xk; C is the circle: x2 + y2 = 9, z = 4,
    oriented counterclockwise as viewed from above.

    © BrainMass Inc. brainmass.com March 4, 2021, 8:37 pm ad1c9bdddf
    https://brainmass.com/math/integrals/integrals-moment-of-inertia-and-stokes-theorem-180872

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    Solution Summary

    This is a series of calculus problems that involve Stokes theorem, finding volume of solids, and moment of inertia

    $2.49

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