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    Multivariable Calculus : Double Integral - Polar Coordinate

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    ( ∫ ^n_r means that n is on the top of the ∫ and r is on the bottom) Evaluate the given integral by first converting to polar coordinates:
    ∫ ^2_1 ∫ ^(square root of 2x - x^2)_0 (1/(square root of x^2 + y^2)) dy dx

    ∫: is the integral symbol

    © BrainMass Inc. brainmass.com March 4, 2021, 5:53 pm ad1c9bdddf
    https://brainmass.com/math/vector-calculus/multivariable-calculus-double-integral-polar-coordinate-16110

    Solution Preview

    I show the same integral like this:

    int(int(1/(sqrt(x^2+y^2),y=sqrt(2x-x^2)..0),x=1..2)

    First we must solve

    int(1/(sqrt(x^2+y^2),y=sqrt(2x-x^2)..0) and of course we must ...

    Solution Summary

    A double integral is solved. The polar coordinates are analyzed.

    $2.49

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