The area bounded by the curve $y=4 x-x^2$ and X - axis in square units, is $\qquad$

The Cartesian equation of the plane $\overline{\mathrm{r}}=(2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}})+\lambda(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-\hat{\mathrm{k}})+\mu(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}})$ is

If the line $\frac{x-3}{2}=\frac{y+5}{-1}=\frac{z+2}{2}$ lies in the plane $\alpha x+3 y-z+\beta=0$, then values of $\alpha$ and $\beta$ respectively are ….

$$ \int_{\log \frac{1}{2}}^{\log 2} \sin \left(\frac{\mathrm{e}^x-1}{\mathrm{e}^x+1}\right) \mathrm{d} x= $$