Arclength Of Graph Of ln ⁡ ( sec ⁡ ( x ) ) \ln(\sec(x))

Calculus Level 2

Let Γ \Gamma denote the graph of f ( x ) = ln ⁡ ( sec ⁡ ( x ) ) f(x) = \ln(\sec(x)) . What is the arclength of the segment of Γ \Gamma bounded by the points ( 0 , 0 ) (0,0) and ( π 4 , ln ⁡ ( 2 ) ) \left (\dfrac \pi4, \ln(\sqrt{2})\right) ?

ln ⁡ ( 2 + 2 ) \ln(\sqrt{2} + 2) ln ⁡ ( 3 + 1 ) \ln(\sqrt{3} + 1) ln ⁡ ( 2 + 1 ) \ln(\sqrt{2} + 1) ln ⁡ ( 3 + 2 ) \ln(\sqrt{3} + 2)

Sameer Kailasa by Sameer Kailasa , 25, USA

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