What is the arc length of $f(x)=xsinx-cos^2x$ on $x in [0,pi]$ ?

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Answer 1 · 2017-08-16T15:30:27

The arc length $s$ of a function $f(x)$ on $x in[a,b]$ is given by

$s=int_a^bsqrt(1+(f'(x))^2)dx$

Here, $f(x)=xsinx-cos^2x$ so $f'(x)=sinx+xcosx+2cosxsinx$ .

Then, the arc length in question is given by:

$s=int_0^pisqrt(1+(sinx+xcosx+2cosxsinx)^2)dxapprox6.4705$

What is the arc length of f(x)=xsinx-cos^2x f(x)=xsinx-cos^2x on x in [0,pi]x in [0,pi]?