Question:
The value of $\int_{0}^{2 \pi}[\sin 2 x(1+\cos 3 x)] d x$, where $[t]$
denotes the greatest integer function, is :
Correct Option: , 3
Solution:
$I=\int_{0}^{2 \pi}[\sin 2 x(1+\cos 3 x)] d x$
$I=\int_{0}^{\pi}([\sin 2 x+\sin 2 x \cos 3 x]+[-\sin 2 x-\sin 2 x \cos 3 x]) d x$
$=\int_{0}^{\pi}-\mathrm{dx}=-\pi$