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March 25, 2017

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Find the arc length of the graph of the function over the indicated interval. (Round your answer to three decimal places.)
y = ln (sin(x))
,[π/4,3π/4]

  • calculus - ,

    y = ln sinx
    y' = 1/sinx * cosx = tanx

    s = Int(sqrt(1+(y')^2)dx)[pi/4,3pi/4]
    = Int(sqrt(1+tan^2(x))dx)[pi/4,3pi/4=
    = Int(secx dx)[pi/4,3pi/4]
    = ln|secx + tanx|[pi/4,3pi/4]
    = ln|-1/√2 + 1| - ln|1/√2 + 1|
    = ln|(1-√2/(1+√2)|
    = ln|2√2-3|
    = ln(3-2√2)

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