The value of $\int_0^{16π/3}|\sin x|dx$ is

17/2 19/2 21/2 none of these

21/2

Let $I =\int_0^{16π/3}|\sin x|dx=\int_0^{5π+\frac{π}{3}}|\sin x|dx$ $=\int_0^{5π}|\sin x|dx+\int_{5π}^{5π+\frac{π}{3}}|\sin x|dx$ $=5\int_0^{π}\sin x\, dx+\int_0^{π/3}\sin x\, dx$ $=5[-\cos x]_0^{π}+[-\cos x]_0^{π/3}$ $= 5 (–1 –1) –(\frac{1}{2}-1)= 10 + 1 –\frac{1}{2}=\frac{21}{2}$