Question

Find the area bounded by the curve $y=sinx$ with x-axis between $x=0$ to x = 2$\pi$.

• A. 4 sq. unit
• B. 8 s q . unit
• C. 4$\pi 4$ sq. unit
• D. 8$\pi 4$ sq. unit

Answer 1

The correct option is A 4 sq. unit

Consider the problem

We have to draw the graph of $y=sinx$

Therefore,

Required area $=AreaOABO+AreaBCDB$

$\begin{array}{c}={\int }_0^{\pi }\sin xdx+\left|{\int }_{\pi }^{2\pi }\sin xdx\right|\\ ={{\left[-\cos x\right]}_0}^{\pi }+\left|{{\left[-\cos x\right]}_{\pi }}^{2\pi }\right|\\ =\left[-\cos \pi +\cos 0\right]+\left|-\cos 2\pi +\cos \pi \right|\\ =1+1+\left|\left(-1-1\right)\right|\\ =2+\left|-2\right|\\ =2+2\\ =4units\end{array}$