Yesterday I asked a question about a certain integral. In the integral is the term:

$$\max\left\{0,\left|\text{n}\cdot\sin\left(2\pi\cdot x\cdot t-\frac{\pi}{2}\right)\right|-2\cdot\text{z}\right\}\tag1$$

I know that $x$, $\text{z}$ and $\text{n}$ are all real and positive numbers.

Next to that I know that the integral is between certain boundaries (where only the lower bound is important for the function that I stated in equation $(1)$). I know that:

$$\frac{1}{4x}\le t<\frac{1}{2x}\tag2$$

Question: is there a way to rewrite equation $(1)$ using the condition that is stated in equation $(2)$ so that I lose the $\max\left\{0,\dots\right\}$ function? If that is possible I can use that to evalute the integral using Mathematica more easily.

  • $\begingroup$ the function $\max(0,x)$ can be written $(|x|+x)/2$, does that help? $\endgroup$ – Calvin Khor Mar 20 at 18:56
  • $\begingroup$ @CalvinKhor Where does that relation come from? I've never seen that. $\endgroup$ – Jan Mar 20 at 18:58
  • 1
    $\begingroup$ well, when $x\ge 0$, then $|x|=x$, and when $x<0$, $|x|=-x$. $\endgroup$ – Calvin Khor Mar 20 at 18:59

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