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)