Question

The value of $\underset{0}{\overset{10\pi }{\int }}|\sin x|dx$ is

• A. $20$
• B. $8$
• C. $10$
• D. $18$

Answer 1

The correct option is A $20$

Let $I=\underset{0}{\overset{10\pi }{\int }}|\sin x|dx$
Using the properties:
$\underset{0}{\overset{nT}{\int }}f\left(x\right)dx=n\underset{0}{\overset{T}{\int }}f\left(x\right)dx\left(T\text{is the period of}f\right(x\left)\right)$
$\Rightarrow I=10\underset{0}{\overset{\pi }{\int }}|\sin x|dx=10\underset{0}{\overset{\pi }{\int }}\sin xdx\therefore I=10[-\cos x{]}_0^{\pi }=20$