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21-11-2016
Mathematics

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

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Nirina7 Nirina7

24-11-2016

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 < x < pi/4 1>U>sqrt 2/2 1>U>sqrt 2/2

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