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10 April, 05:58

Find the arc length of the curve y = ln (cos x) for 0 < x < pi/4

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  1. 10 April, 06:14
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    The solution is

    L = S (ln (cos x)) 'dx = S (-sinx / cosx) dx =

    0 < x < pi/4 0 < x < pi/4

    let be U=cosx dU = - sinxdx

    so

    S (-sinx / cosx) dx = SdU/U = LnU = 0-1/2ln2-ln2 = 1/2) Ln2

    0 sqrt 2/2 1>U>sqrt 2/2
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