Question

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

Answer 1

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`