Single Variable Calculus, Chapter 5, 5.4, Section 5.4, Problem 42

Find the integrals $\displaystyle \int^{3\pi/2}_0 |\sin x| dx$

$
\begin{equation}
\begin{aligned}
\int^{3\pi/2}_0 |\sin x| dx &= \int^{\pi}_0 \sin x dx + \int^{3\pi/2}_{\pi} - \sin x dx\\
\\
\int^{3\pi/2}_0 |\sin x| dx &= \left( \int^{\pi}_0 \sin x dx - \int^{\pi}_0 \sin x dx \right) + \left( \int^{3\pi/2}_{\pi} - \sin x dx - \int^{3\pi/2}_{\pi} - \sin x dx\right)\\
\\
\int^{3\pi/2}_0 |\sin x| dx &= \left[ - \cos (\pi) - \left[ - \cos (0) \right] + \left[ - \left( - \cos \frac{3 \pi}{2} \right) + (-\cos \pi) \right] \right]\\
\\
\int^{3\pi/2}_0 |\sin x| dx &= 1 + 1 + 0 + 1\\
\\
\int^{3\pi/2}_0 |\sin x| dx &= 3
\end{aligned}
\end{equation}
$