The area bounded by $\mathrm{y} = {\sin }^{-1}\left(\mathrm{x}\right), \mathrm{x} = \frac{1}{\sqrt{2}}$and x - axis is

• $\left(\frac{1}{\sqrt{2}} + 1\right)\mathrm{sq} \mathrm{unit}$

• $\left(1 - \frac{1}{\sqrt{2}}\right)$ sq unit

• $\frac{\mathrm{\pi }}{4\sqrt{2}}$ sq unit

• $\left(\frac{\mathrm{\pi }}{4\sqrt{2}} + \frac{1}{\sqrt{2}} - 1\right) \mathrm{sq} \mathrm{unit}$

The area between the curve y = 1 - $\left|\mathrm{x}\right|$ and the x-axis is equal to

• 1 sq unit

• $\frac{1}{2}$ sq unit

• $\frac{1}{3}$

• 2 sq unit

The value of ${\int }_{{\mathrm{e}}^{-1}}^{\mathrm{e}}\frac{\mathrm{dt}}{\mathrm{t}\left(1 + \mathrm{t}\right)}$ is equal to

• 0

• $\log \left(\frac{\mathrm{e}}{1 + \mathrm{e}}\right)$

• $\log \left(\frac{1}{1 + \mathrm{e}}\right)$

• 1

The figure shows a triangle AOB and the parabola y = x². The ratio of the area of the triangle AOB to the area of the region AOB of the parabola y = x is equal to

• $\frac{3}{5}$

• $\frac{3}{4}$

• $\frac{7}{8}$

• $\frac{5}{6}$

The area of the plane region bounded by the curve x = y² - 2 and the· line y = - x is (in square units)

• $\frac{13}{3}$

• $\frac{2}{5}$

• $\frac{9}{2}$

• $\frac{5}{2}$

The area bounded by the curve y = sin(x) between x = 0 and x = 2$\mathrm{\pi }$ is (in square units)

• 1

• 2

• 0

• 4

The area bounded by y = x + 2, y = 2 - x and the x-axis is (in square units)

• 1

• 2

• 4

• 6

168.

Area bounded by the curve y = log (x - 2), x-axis and x = 4 is equal to

• 2log(2) + 1

• log(2) - 1

• log(2) + 1

• 2log(2) - 1

Area bounded by the curves y = e^x, y = e^{- x} and the straight line x = 1 is (in sq units)

• $\mathrm{e} + \frac{1}{\mathrm{e}}$

• $\mathrm{e} + \frac{1}{\mathrm{e}} + 2$

• $\mathrm{e} + \frac{1}{\mathrm{e}} - 2$

• $\mathrm{e} - \frac{1}{\mathrm{e}} + 2$

The area (in sq units) bounded by y = x² + 3 and y = 2x + 3 is

• $\frac{12}{7}$

• $\frac{4}{3}$

• $\frac{3}{4}$

• $\frac{8}{3}$