11.

The area (in sq. units) of the region A =  is :

• $\frac{53}{6}$

• 8

• $\frac{26}{3}$

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

(where c is a constant of integration)

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

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

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

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