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Find out the length of y = ln(sec x ) between 0 < x < π/4.
Solution
In this example we'll need to use the first ds as the function is in the form y = f (x). So, let us get the derivative out of the way.
Dy/dx
= sec x tan x / secx = tan x (dy/dx)2 = tan2 x
Let's as well get the root out of the way as there is frequently simplification that can be done and there is no cause to do that in the integral.
√ (1 + (dy/dx)2)
= √ (1+ tan2 x)
= √ (sec2 x )
= |sec x|
= sec x
Note: we could drop the absolute value bars here because secant is positive in the range given. After that the arc length is
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