The value of $\int\limits_{-\pi / 6}^{\pi / 6}\left(4 x^5+x \sin ^2 x+\tan ^3 x+2\right) dx$ is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\frac{2 \pi}{3}$
$I=\int\limits_{-\pi / 6}^{\pi / 6}\left(4 x^5+x \sin ^2 x+\tan ^3 x+2\right) dx$
$4 x^5+x \sin ^2 x+\tan ^3 x$ → odd function
2 → even function
$I=\int\limits_{-\pi / 6}^{\pi / 6}0+2dx$
$=2×\frac{\pi}{3}=\frac{2 \pi}{3}$