1. Calculate: Ò $\arcsin (\cos x) d x$, if $x$ Î $[0,2 p]$

Note: The symbols "Ò" and "Î" are not standard in English mathematical notation. They are likely meant to represent the integral sign (∫) and the "is in" symbol (∈), respectively. Thus, the more conventional representation would be:

1. Calculate: ∫ $\arcsin (\cos x) d x$, if $x$ ∈ $[0,2 \pi]$
1. Calculate: Ò $\arcsin (\cos x) d x$, if $x$ Î $[0,2 p]$

## Solution

![](https://cdn.mathpix.com/cropped/2024_06_07_cf04f506e879809b58f0g-2.jpg?height=235&width=1026&top_left_y=606&top_left_x=91)

$\Rightarrow$ Ò $\arcsin (\cos x) d x=\frac{\frac{1}{1} \frac{p x-x^{2}}{2}+c, x \hat{\mathrm{I}}[0, p]}{\frac{1}{\frac{1}{2}} \frac{x^{2}-3 p x}{2}+p^{2}+c, x \hat{\mathrm{I}}(p, 2 p]}$, where $c \hat{\mathrm{I}}$;