Question

Evaluate ${\int }_0^{16\pi /3}\left|\sin x\right|dx$

Answer 1

$\frac{16\pi }{3}=5\pi +\frac{\pi }{3}$

${\int }_0^{16\pi /3}|\sin x|dx=5{\int }_0^{\pi }\sin xdx+{\int }_0^{\pi /3}\sin xdx$

$=5[-\cos x{]}_0^{\pi }+[-\cos {]}_0^{\pi /3}$

$=10+1/2$

$=\frac{21}{2}=10.5$