How do you find the arc length of the curve #y=lncosx# over the interval [0, pi/3]?
2 Answers
Jun 23, 2018
Explanation:
so we have
Note that
Jun 25, 2018
Explanation:
#y=ln(cosx)#
#y'=-tanx#
Arc length is given by:
#L=int_0^(pi/3)sqrt(1+tan^2x)dx#
Simplify:
#L=int_0^(pi/3)secxdx#
Integrate directly:
#L=[ln|secx+tanx|]_0^(pi/3)#
Insert the limits of integration:
#L=ln(2+sqrt3)#