The area (in sq. units) of the region A = $\left\{\left(\mathrm{x}, \mathrm{y}\right) \ge \mathrm{R} \times \mathrm{R} | 0 \le \mathrm{x} \le 3, 0 \le \mathrm{y} \le 4, \mathrm{y} \le {\mathrm{x}}^2 + 3\mathrm{x}\right\}$ is :

• $\frac{59}{6}$

• $\frac{53}{6}$

• 8

• $\frac{26}{3}$

12.

$\int \frac{\sin \left({\displaystyle \frac{5\mathrm{x}}{2}}\right)}{\sin \left({\displaystyle \frac{\mathrm{x}}{2}}\right)}\mathrm{dx}$ is equal to :

(where c is a constant of integration)

• $\mathrm{x} + 2\sin \left(\mathrm{x}\right) + 2\sin \left(2\mathrm{x}\right) + \mathrm{c}$

• $2\mathrm{x} + \sin \left(\mathrm{x}\right) + \sin \left(2\mathrm{x}\right) + \mathrm{c}$

• $2\mathrm{x} + \sin \left(2\mathrm{x}\right) + 2\sin \left(\mathrm{x}\right) + \mathrm{c}$

• $\mathrm{x} + \sin \left(2\mathrm{x}\right) + 2\sin \left(\mathrm{x}\right) + \mathrm{c}$