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 $=\displaystyle\int_{x=0}^{x=3 \pi} y d x=\displaystyle\int_{0}^{3 \pi} \sin \left(\frac{x}{3}\right) d x$
Let $\frac{x}{3}=t $
$\Rightarrow d x=3 d t$
Also, when $x=0$
Then, $ t=0$
When $x=3 \pi$
Then $ t=\pi$
Then, required area
$=\displaystyle\int_{0}^{\pi} \sin t(3 d t)=3[-\cos t]_{0}^{\pi}$
$=-3[\cos \pi-\cos 0]$
$=-3(-1-1)=-3(-2)=6$