### Application of Integrals

goals
Sketch the graph for $y={\csc}^{-1}\left(csc{x}\right)$
Consider a square with vertices at $A\left(1,1\right),B\left(-1,1\right),C\left(-1,-1\right)$ and $D\left(1,-1\right)$.Let $S$ be the region consisting of all points inside the square which are nearer to the origin than to any edge.
On the basis of above information, answer the following questions:
Consider a square with vertices at $A\left(1,1\right),B\left(-1,1\right),C\left(-1,-1\right)$ and $D\left(1,-1\right)$.Let $S$ be the region consisting of all points inside the square which are nearer to the origin than to any edge.
On the basis of above information, answer the following questions:
Find the solutions of $4\left\{x\right\}=x+\left[x\right]$ where $\left\{.\right\},\left[.\right]$ represents fractional part and greatest integer function.
Solve $y = \left| {\cos x} \right|,\,y = 0,\,x = - \pi$ and $x = \pi$