Question

The area bounded by $y=\left|\sin \left(x\right)\right|$, $x-axis$ and the lines $\left|x\right|=\mathrm{\pi }$ is

• A. $2squnits$
• B. $3squnits$
• C. $4squnits$
• D. None of these

Answer 1

The correct option is C

$4squnits$

Given

$$\begin{gathered} \left|x\right|=\mathrm{\pi } \\ \Rightarrow \mathrm{x}=-\mathrm{\pi },\mathrm{\pi } \end{gathered}$$

The area bounded

$$\begin{gathered} y={\int }_{-\mathrm{\pi }}^{\mathrm{\pi }}\sin \left(x\right)dx \\ y=2{\int }_0^{\mathrm{\pi }}\sin xdx \\ y=2{\left[-\cos \left(x\right)\right]}_0^{\mathrm{\pi }} \\ y=-2\left[\cos \left(\mathrm{\pi }\right)-\cos \left(0\right)\right] \\ y=-2\left[-1-1\right]\because \cos \left(\mathrm{\pi }\right)=-1and\cos \left(0\right)=1 \\ y=-2\left(-2\right) \\ y=4squnits \end{gathered}$$

Hence, the area bounded is $4squnits$.