Find the length of the curve Arc length Solutiony sinxcosx

Find the length of the curve

Arc length =

Solution

y\' = -sinx/cosx = -tanx
arc length
= (1+y\'^2)dx, from 0 to pi/3
= secx dx, from 0 to pi/3
= secx (secx+tanx)/(secx + tanx) dx, from 0 to pi/3
= ln|secx+tanx|, from 0 to pi/3
= ln(2+3)