Question

The value of $\underset{0}{\stackrel{16\pi /3}{\int }}|\sin x|dx$ is

• A. $21$
• B. $\frac{21}{2}$
• C. $10$
• D. $\frac{10}{2}$

Answer 1

Answer: (B)

$\frac{21}{2}$

${\int }_0^{16\frac{\pi }{3}}|\sin x|dx$

$={\int }_0^{\pi }\sin xdx+{\int }_{\pi }^{2\pi }-\sin xdx+{\int }_{2\pi }^{3\pi }\sin xdx+{\int }_{3\pi }^{4\pi }-\sin xdx+{\int }_{4\pi }^{5\pi }\sin xdx+{\int }_{5\pi }^{16\frac{\pi }{3}}-\sin xdx$

$=2+2+2+2+2+\frac{1}{2}$

$=\frac{21}{2}$