Arc length of the curve

Question

Find the arc length of the curve y = ln ⁡(cos ⁡x) from x = 0 to x=pi/6

Answer 1

Arc length = ∫_{(from a to b)} √ (1 + (dy/dx)²) dx

So, we have ∫_{(from 0 to π/6)} √ (1 + tan²x) dx = ∫_{(from 0 to π/6)} secx dx =

ln(secx + tanx)_{from 0 to π/6)} = ln(2/√3 + 1/√3) = ln√3 = (1/2)ln3