List of top Statistics Questions on Double and triple integrals

If $f(x)=\begin{cases}\frac{\log_{e}(1+\frac{x}{a})-\log_{e}(1-\frac{x}{b})}{x}& if~x\ne0\\k& if~x=0\end{cases}$ is continuous at $x=0$, then value of $k$ is:

The value of integral $\int_{0}^{1}\int_{x}^{1}\frac{1}{1+y^{2}}\cdot dydx$ is equal to

The area of region in the first quadrant that is bounded by $y=\sqrt{x}$, $y=2-x$ and x-axis is

Integral $\int_{0}^{2}\int_{y^{2}}^{y+2} dxdy$ equals