Compute the Riemann integral of the absolute value of sinx from 0 to 2(pi)
We note that,Originally Posted by TexasGirl
$\displaystyle f=|\sin x|$ is countinous thus it exists.
If $\displaystyle 0\leq x\leq \pi$
Then, $\displaystyle f=\sin x$ by the definition of absolute value.
If $\displaystyle \pi \leq x\leq 2\pi$
Then, $\displaystyle f=-\sin x$ by the definition of absolute value.
Thus, by the subdivision rule,
$\displaystyle \int_0^{2\pi}|\sin x|dx=\int_0^{\pi}\sin xdx+\int_{\pi}^{2\pi} -\sin xdx$
I assume you can solve it from heir.