How do you find the arc length of the curve $y=sqrt(cosx)$ over the interval [-pi/2, pi/2]?

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Answer 1 · 2017-01-14T20:22:19

The arc element of the curve $y=f(x)$ is given by the expression:

$dl = sqrt(dx^2+dy^2) = sqrt(dx^2+(f'(x)dx)^2) =dx sqrt(1+(f'(x))^2)$

as:

$f(x) = sqrt(cosx)$

$f'(x) = sinx/(2sqrt(cosx))$

integrating over the interval we have:

$l =int_(-pi/2)^(pi/2) sqrt (1+sin^2x/(2cosx))dx$

How do you find the arc length of the curve y=sqrt(cosx)y=sqrt(cosx) over the interval [-pi/2, pi/2]?