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    Polar Coordinates and Change Order of Integration; Volume of an Ellipsoid; Change of Variables on Continuous Function of One Variable

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    Assuming r, θ are the polar coordinates, change the order of integration:
    ∫-pi/2-->pi/2 ∫0-->a cos θ f(r, θ ) dr dθ

    Find the volume of the ellipsoid: x^2/a^2 + y^2/b^2 + z^2/c^2 ≤ 1

    Let a and b be any numbers such that a^2 + b^2 =1 and f(x,y) be a continuous function of one variable. Perform the change of variables :
    {u =ax +by
    {v=bx - ay

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    https://brainmass.com/math/integrals/polar-coordinates-change-order-integration-volume-64912

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    In the polar system, the region of integration is: , for ...

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    Polar Coordinates and Change Order of Integration; Volume of an Ellipsoid; Change of Variables on Continuous Function of One Variable are investigated. The solution is detailed and well presented.

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