The value of ∫_0^16π/3|sin x|dx is

Let $I =\int_0^{16π/3}|\sin x|dx=\int_0^{5π+\frac{π}{3}}|\sin x|dx$

$=\int_0^{5π}|\sin x|dx+\int_{5π}^{5π+\frac{π}{3}}|\sin x|dx$

$=5\int_0^{π}\sin x\, dx+\int_0^{π/3}\sin x\, dx$

$=5[-\cos x]_0^{π}+[-\cos x]_0^{π/3}$

$= 5 (–1 –1) –(\frac{1}{2}-1)= 10 + 1 –\frac{1}{2}=\frac{21}{2}$