Mathematics : Application of Integrals

The area bounded by the curve y = $\sin \left(\frac{\mathrm{x}}{3}\right)$, x-axis and lines x = 0 and z = 3$\mathrm{\pi }$ is

• 9

• 0

• 6

• 3

The area of the region bounded by the lines y = mx, x = 1, x = 2 and x-axis is 6 sq units, then 'm' is

• 3

• 1

• 2

• 4

Area bounded by y = x³, y = 8 and x = 0 is

• 12 sq units

• 2 sq units

• 6 sq units

• 14 sq units

Area lying between the curves y² = 2x and y = x is

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

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

• $\frac{1}{4} \mathrm{sq} \mathrm{unit}$

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

The area of the region bounded by the curve y = x² and the line y = 16

• $\frac{64}{3} \mathrm{sq} \mathrm{unit}$

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

• $\frac{256}{3} \mathrm{sq} \mathrm{unit}$

• $\frac{128}{3} \mathrm{sq} \mathrm{unit}$

Area of the region bounded by the curve y = cos(x), x = 0 and x = $\mathrm{\pi }$ is

• 4 sq unit

• 3 sq units

• 1 sq units

• 2 sq units

The area bounded by the curves y² - x = 0 and y - x² = 0, is

• 7/3 sq unit

• 1/3 sq unit

• 5/3 sq unit

• 1 sq unit

Area between the curve y = cos(x) and X - axis, when $0 \le \mathrm{x} \le 2\mathrm{\pi }$, is

• 0 sq units

• 2 sq units

• 3 sq units

• 4 sq units

The area bounded by the X - axis, the curve y = f(x) and the lines x = 1, x = b and is equal to $\sqrt{{\mathrm{b}}^2 + 1} - \sqrt{2}$ for all b > 1, then f(x) is

• $\sqrt{\mathrm{x} - 1}$

• $\sqrt{\mathrm{x} + 1}$

• $\sqrt{{\mathrm{x}}^2 + 1}$

• $\frac{\mathrm{x}}{\sqrt{1 + {\mathrm{x}}^2}}$

Area bounded by the curve xy - 3x - 2y - 10 = 0, X-axis and the lines x = 3, x = 4 is

• $16\log \left(2\right) - 13 \mathrm{sq} \mathrm{unit}$

• $16\log \left(2\right) - 3 \mathrm{sq} \mathrm{unit}$

• $16\log \left(2\right) + 3 \mathrm{sq} \mathrm{unit}$

• None of the above