The area between the parabola y = x² and the line y = x is : 

• $\frac{1}{6} \mathrm{sq} \mathrm{unit}$

• $\frac{1}{3} \mathrm{sq} \mathrm{unit}$

• $\frac{1}{2} \mathrm{sq} \mathrm{unit}$

• None of these

112.

The area enclosed between the curves y = x³ and y = $\sqrt{\mathrm{x}}$ is, (in square units)

• $\frac{5}{3}$

• $\frac{5}{4}$

• $\frac{5}{12}$

• $\frac{12}{5}$

The area included between the parabolas x² = 4y and y² = 4x is (in square units)

• $\frac{4}{3}$

• $\frac{1}{3}$

• $\frac{16}{3}$

• $\frac{8}{3}$

The area of the figure bounded by the curves y = cos(x) and y = sin(x) and the coordinate x = 0 and x = $\frac{\mathrm{\pi }}{4}$

• $\sqrt{2} + 1$

• $\sqrt{2} - 1$

• $\frac{1}{\sqrt{2}}$

• $\frac{\sqrt{2} - 1}{\sqrt{2}}$

The area bounded by the parabola y² = 4ax and the line x = a and x = 4a is

• $\frac{35{\mathrm{a}}^2}{3}$

• $\frac{4{\mathrm{a}}^2}{3}$

• $\frac{7{\mathrm{a}}^2}{3}$

• $\frac{56{\mathrm{a}}^2}{3}$

The area of the region bounded by the curve 9x² + 4y² - 36 = 0 is

• $9\mathrm{\pi }$

• $5\mathrm{\pi }$

• $36\mathrm{\pi }$

• $6\mathrm{\pi }$

The area enclosed between the parabola y = x² - x + 2 and the line y = x + 2 in sq unit equals :

• $\frac{8}{3}$

• $\frac{1}{3}$

• $\frac{2}{3}$

• $\frac{4}{3}$

The area bounded by the curve x = 4 - y² and the Y-axis is

• 16 sq units

• 32 sq units

• $\frac{32}{3} \mathrm{sq} \mathrm{units}$

• $\frac{16}{3} \mathrm{sq} \mathrm{units}$

The area of the region bounded by y = 2x - x² and the x-axis is

• $\frac{8}{3} \mathrm{sq} \mathrm{unit}$

• $\frac{4}{3} \mathrm{sq} \mathrm{unit}$

• $\frac{7}{3} \mathrm{sq} \mathrm{unit}$

• $\frac{2}{3} \mathrm{sq} \mathrm{unit}$

The area bounded between the parabola y² = 4x and the line y = 2x - 4 is equal to

• $\frac{17}{3} \mathrm{sq} \mathrm{unit}$

• $\frac{19}{3} \mathrm{sq} \mathrm{unit}$

• 9 sq unit

• 15 sq unit