How do I find the arc length of the curve #y=ln(sec x)# from #(0,0)# to #(pi/ 4, ln(2)/2)#?

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Answer 1 · 2018-05-31T10:30:35

#L=ln(1+sqrt2)# units.

#y=ln(secx)#

#y'=tanx#

Arc length is given by:

#L=int_0^(pi/4)sqrt(1+tan^2x)dx#

Simplify:

#L=int_0^(pi/4)secthetad theta#

Integrate directly:

#L=[ln|sectheta+tantheta|]_0^(pi/4)#

Hence

#L=ln(1+sqrt2)#