Find the area bounded by
(i) y$={\log }_e\left|x\right|\text{and}y=0$
(ii) $y=\left|{\log }_e\left|x\right|\right|\text{and}y=0$

Find the area bounded by the curve $x=\{\begin{array}{cc}-2-y\text{,}& y<-1\\ y^3\text{,}& -1\le y\le 1\\ 2-y\text{,}& y>1\end{array}$ and x=0 is

Find the area bounded by the curves $y=x^3-x\text{and}y=x^2+x.$

Find the area bounded by $y=-x^3+x^2+16x\text{and}y=4x$

Find the area of the region enclosed by the curves y= x log x and $y=2x-2x^2$.

Find the area of the region bounded by the curves $y=\sqrt{x+2}\text{and}y=\frac{1}{x+1}$ between the lines x=0 and x=2.

Find the area bounded by $y^2\le 4x,x^2+y^2\ge 2x,\text{and}x\le y+2$ in the first quadrant.

The area common to regions $x^2+y^2-2x\le 0\text{and}y\ge \frac{\sin \left(\pi x\right)}{2}.$

Find the area of the region enclosed by $y=-5x-x^2\text{and}y=x$ on interval $\left[-1,5\right]$

Find the area enclosed by the graph of $y={\log }_e\left(x+1\right),$y-axis, and the line y=1