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I'm having trouble with this integral
$$\int\arcsin(\sin x)\,\mathrm dx$$

The problem is with the intervals of definition for each function :/ if someone could dumb it down for me.

  • $\arcsin\colon [-1, 1] \to [-\pi/2, \pi/2]$.
  • $\sin:\mathbb{R}\to [-1, 1]$.

right?

But what about $\arcsin(\sin x)$ ?

  • 0
    Note that the arcsine has range $[-\frac{\pi}{2},\frac{\pi}{2}]$, $\sin(x+\pi)=-\sin\;x$, and that $\sin\;x$ has period $2\pi$...2010-12-12
  • 3
    As a matter of fact, why not try [plotting it](http://tinyurl.com/34f2qzn) and see for yourself?2010-12-12

3 Answers 3