The value of _0^ / 6 3 x d x is:

MCQ

The value of $\int_0^{\pi / 6} \sin 3 x d x$ is:

A
$-\frac{\sqrt{3}}{2}$
B
$-\frac{1}{3}$
C
$\frac{\sqrt{3}}{2}$
✓
$\frac{1}{3}$

✓

Answer

Correct option: D.

$\frac{1}{3}$

$\text {Let } I=\int_0^{\pi / 6} \sin 3 x d x$
$=\frac{-1}{3}[\cos 3 x]_0^{\pi / 6}$
$=\frac{-1}{3}\left[\cos \frac{\pi}{2}-\cos 0\right]=\frac{-1}{3}(0-1)=\frac{1}{3}$

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