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Find the arc length of the curve y = ln (cos x) for 0 < x < pi/4
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Oct 13, 2017
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Find the arc length of the curve y = ln (cos x) for 0 < x < pi/4
Mathematics
high-school
Jason Gabel
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Jason Gabel
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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 < x < pi/4 1>U>sqrt 2/2 1>U>sqrt 2/2
Mesco
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Oct 17, 2017
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Mesco
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