1.

What is the area of one of the loops between the curve      y = csin(x) and x-axis ?

• c

• 2c

• 3c

• 4c

Consider the curves

$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right) = \mathrm{x}\left|\mathrm{x}\right| - 1 \mathrm{and} \mathrm{g}\left(\mathrm{x}\right) = \left\{\frac{3\mathrm{x}}{2}, \mathrm{x} > 0 \\ 2\mathrm{x}, \mathrm{x} \le 0\right\} \end{gathered}$$

What is the area bounded by the curves ?

• $\frac{17}{6}$ square units

• $\frac{8}{3}$ square units

• 2 square units

• $\frac{1}{3}$ square units

Consider the function

$\mathrm{f}\left(\mathrm{x}\right) = \left|\mathrm{x} - 1\right| + {\mathrm{x}}^2$

where, x $\in \mathrm{ℝ}$

What is the area of the region bounded by x-axis, the curve y = f(x) and the two ordinates x = $\frac{1}{2}$ and x = 1 ?

• $\frac{5}{12}$ square unit

• $\frac{5}{6}$ square unit

• $\frac{7}{6}$ square unit

• 2 square unit

Consider the curves

$\mathrm{y} = \left|\mathrm{x} - 1\right| \mathrm{and} \left|\mathrm{x}\right| = 2$

What is/are the point(s) of intersection of the curves ?

• ( - 2, 3) only

• (2, 1) only

• ( - 2, 3) and (2, 1)

• Neither ( - 2, 3) nor (2, 1)

Consider the curves

$\mathrm{y} = \left|\mathrm{x} - 1\right| \mathrm{and} \left|\mathrm{x}\right| = 2$

What is the area of the region bounded by the curves and x-axis ?

• 3 square unit

• 4 square unit

• 5 square unit

• 6 square unit

What is the area bounded by the curves $\left|\mathrm{y}\right| = 1 - {\mathrm{x}}^2 ?$

• $\frac{4}{3}$ square units

• $\frac{8}{3}$ square units

• $4$ square units

• $\frac{16}{3}$ square units

What is the area of the region boundedby |x| < 5, y = 0 and y = 8 ?

• 40 square units

• 80 square units

• 120 square units

• 160 square units