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∫_0^(1/2)xdx/√(1-x²)

  • mathematics - ,

    ∫_0^(1/2)xdx/√(1-x²)

    I do not know what
    0^(1/2)
    is. It is probably a symbol that I do not have.

    Integral of x dx/sqrt(1-x^2)

    let x = sin t
    then dx = cos t dt
    1-x^2 = 1 -sin^2 t = cos^2 t
    so
    integral of
    sin t cos t dt / cos t
    = integral of
    sin t dt
    =-cos t
    but
    -cos t = -sqrt(1-x^2)

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