Question

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

• A. 9
• B. 0
• C. 6
• D. 3

Answer 1

Answer: (C)

Area $=\underset{0}{\overset{3\pi }{\int }}\sin \left(\frac{x}{3}\right)dx$
put $\frac{x}{3}=t$
$dx=3\times dt$
$=\underset{0}{\overset{\pi }{\int }}\sin t.3dtx=0,3\pi \Rightarrow t=0,\pi$
$=3(-\cos t{)}_0^{\pi }$
$=3[1+1]=6$ square units