Thank you for reporting, we will resolve it shortly
Q.
The value of $\int\limits_{0}^{V}|\sin x| d x$ where $n$ is a positive integer and $V \in[2 n \pi,(2 n+1) \pi], n \in N$ is
Integrals
Solution:
$I=\int\limits_{0}^{V}|\sin x| d x=\int\limits_{0}^{2 n \pi}|\sin x| d x+\int\limits_{2 n \pi}^{V}|\sin x| d x$
Now, $|\sin x|$ has period $\pi$ and $V$ lies in 1 st quadratnt
Then, $I=2 n \int\limits_{0}^{\pi} \sin x d x+\int\limits_{2 n \pi}^{V} \sin x d x$
$=4 n+[-\cos x]_{2 n \pi}^{V}=4 n+1-\cos V$