Question

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

• A. 9
• B. 0
• C. 6
• D. 3

Answer 1

Answer: (C)

Required area $={\int }_{x=0}^{x=3\pi }ydx={\int }_0^{3\pi }\sin \left(\frac{x}{3}\right)dx$
Let $\frac{x}{3}=t$
$\Rightarrow dx=3dt$
Also, when $x=0$
Then, $t=0$
When $x=3\pi$
Then $t=\pi$
Then, required area
$={\int }_0^{\pi }\sin t(3dt)=3[-\cos t{]}_0^{\pi }$
$=-3[\cos \pi -\cos 0]$
$=-3(-1-1)=-3(-2)=6$