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

• A

  9 sq. units
• B

  $\frac{1}{3}$ sq. units
• Correct answer
  C

  6 sq. units
• D

  3 sq. units

Solution

$\begin{aligned} & \int_0^{3 \pi} \sin \left(\frac{x}{3}\right) d x \\ & \left(-3 \cdot \cos \frac{x}{3}\right)_0^{3 \pi}=(-3(-1))-(-3(1))=6\end{aligned}$

Hence, the correct answer is option: 'C'.