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

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