What is the arclength of $f(x)=cos^2x-x^2$ in the interval $[0,pi/3]$ ?

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Answer 1 · 2015-11-15T15:55:42

arc length $=intsqrt[1+(dy/dx)^2]$

$dy/dx=-2cosx(sinx)-2x$

$int_0^(pi/3)sqrt[1+(-2cosxsinx-2x)^2dx]~~2.20$

(Note: Used TI-84 calculator to integrate)

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What is the arclength of f(x)=cos^2x-x^2 f(x)=cos^2x-x^2 in the interval [0,pi/3][0,pi/3]?