Mathematics : Application of Integrals

The area (in square units) of the region bounded by x² = 8y, x = 4 and X-axis, is

• $\frac{2}{3}$

• $\frac{4}{3}$

• $\frac{8}{3}$

• $\frac{10}{3}$

The area bouned by y = x² + 2, x-axis, x = 1 and x = 2 is

• $\frac{16}{3}$

• $\frac{17}{3}$

• $\frac{13}{3}$

• $\frac{20}{3}$

The area (in square units) bounded by the curves y² = 4x and x² = 4y in the plane is

• $\frac{8}{3}$

• $\frac{16}{3}$

• $\frac{32}{3}$

• $\frac{64}{3}$

The area (in square unit) of the region enclosed by the curves y = x and y = x³ is

• $\frac{1}{12}$

• $\frac{1}{6}$

• $\frac{1}{3}$

• 1

The area (in sq unit) of the region bounded by the curves 2x = y² - 1 and x = 0 is

• $\frac{1}{3}$

• $\frac{2}{3}$

• 1

• 2

The area (in square units) of the region enclosed by the two circles x² + y² = 1 and (x - 1)² + y² = 1 is

• $\frac{2\mathrm{\pi }}{3} + \frac{\sqrt{3}}{2}$

• $\frac{\mathrm{\pi }}{3} + \frac{\sqrt{3}}{2}$

• $\frac{\mathrm{\pi }}{3} - \frac{\sqrt{3}}{2}$

• $\frac{2\mathrm{\pi }}{3} - \frac{\sqrt{3}}{2}$

The values of a function f(x) at different values of x are as follows

x	0	1	2	3	4	5
f(x)	2	3	6	11	18	27

Then, the approximate area (in square units) bounded by the curve y = f(x) and x-axis between x = 0 and 5, using the Trapezoidal rule, is

• 50

• 75

• 52.5

• 62.5

The area (in square units) of the region bounded by the curves x = y² and x = 3 - 2y² is

• $\frac{3}{2}$

• 2

• 3

• 4

The area (in sq units) bounded by the curves y² = 4x and x² = 4y is

• $\frac{64}{3}$

• $\frac{16}{3}$

• $\frac{8}{3}$

• $\frac{2}{3}$

$$\begin{gathered} \mathrm{The} \mathrm{area} \mathrm{of} \mathrm{the} \mathrm{region} \mathrm{described} \mathrm{by} \\ \left\{(\mathrm{x}, \mathrm{y})/{\mathrm{x}}^2 + \mathrm{y} \le 1 \mathrm{and} \mathrm{y} \le 1 - \mathrm{x}\right\} \mathrm{is} \end{gathered}$$

• $\frac{\mathrm{\pi }}{2} - \frac{2}{3}$

• $\frac{\mathrm{\pi }}{2} + \frac{2}{3}$

• $\frac{\mathrm{\pi }}{2} + \frac{4}{3}$

• $\frac{\mathrm{\pi }}{2} - \frac{4}{3}$