The value of ${\int }_2^4\left(\mathrm{x} - 2\right)\left(\mathrm{x} - 3\right)\left(\mathrm{x} - 4\right)\mathrm{dx}$ is equal to

• $\frac{1}{2}$

• 2

• 3

• 0

${\int }_0^{\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\frac{\sqrt{\sin \left(\mathrm{x}\right)}}{\sqrt{\sin \left(\mathrm{x}\right)} + \sqrt{\cos \left(\mathrm{x}\right)}}\mathrm{dx}$ is equal to

• 0

• $- \mathrm{\pi }$

• $\raisebox{1ex}{$3\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

• $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$

${\int }_{2016}^{2017}\frac{\sqrt{\mathrm{x}}}{\sqrt{\mathrm{x}} + \sqrt{4033} - \mathrm{x}}\mathrm{dx}$ is equal to

• 1/4

• 3/2

• 2017/2

• 1/2

${\int }_{- 1}^1\max \left\{\mathrm{x}, {\mathrm{x}}^3\right\}\mathrm{dx}$ is equal to

• 3/4

• 1/4

• 1/2

• 1

$\int \frac{{\mathrm{x}}^2}{1 + {\left({\mathrm{x}}^3\right)}^2}\mathrm{dx}$ is equal to

• ${\tan }^{-1}\left({\mathrm{x}}^2\right) + \mathrm{C}$

• $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.{\tan }^{-1}\left({\mathrm{x}}^3\right) + \mathrm{C}$

• $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.{\tan }^{-1}\left({\mathrm{x}}^3\right) + \mathrm{C}$

• $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.{\tan }^{-1}\left({\mathrm{x}}^2\right) + \mathrm{C}$

${\int }_0^{\mathrm{x}}\mathrm{f}\left(\mathrm{t}\right)\mathrm{dt} = {\mathrm{x}}^2 + {\mathrm{e}}^{\mathrm{x}}$ (x > 0), then f(1) is equal to

• 1 + e

• 2 + e

• 3 + e

• e

$\int \frac{\mathrm{x} + 1}{{\mathrm{x}}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}\mathrm{dx} =$

• - x^3/2 + x^1/2 + C

• x^1/2

• x^3/2 + 2x^1/2 + C

• $\frac{2{\mathrm{x}}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}{3} + 2{\mathrm{x}}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} + \mathrm{C}$

258.

$\int \frac{\mathrm{dx}}{{\mathrm{e}}^{\mathrm{x}} + {\mathrm{e}}^{- \mathrm{x}} + 2}$ is equal to

• $\frac{1}{{\mathrm{e}}^{\mathrm{x}} + 1} + \mathrm{C}$

• $\frac{- 1}{{\mathrm{e}}^{\mathrm{x}} + 1} + \mathrm{C}$

• $\frac{1}{1 + {\mathrm{e}}^{- \mathrm{x}}} + \mathrm{C}$

• $\frac{1}{{\mathrm{e}}^{- \mathrm{x}} - 1} + \mathrm{C}$

${\int }_{- 1}^0\frac{\mathrm{dx}}{{\mathrm{x}}^2 + \mathrm{x} + 2}$ is equal to

• $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$

• $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

• $\mathrm{\pi }$

• $\frac{4}{\sqrt{7}}{\tan }^{-1}\left(\frac{1}{\sqrt{7}}\right)$

${\int }_{- 2}^2\left|1 - {\mathrm{x}}^2\right|\mathrm{dx}$ is equal to :

• 4

• 2

• - 2

• 0