Question

For $0\le x\le \pi$, the area bounded $y=x$ and $y=x+sinx$, is

• A. 2
• B. 4
• C. $2\pi$
• D. $4\pi$

Answer 1

The correct option is A 2

The curves $y=x$ and $y=x+sinx$ intersect at (0, 0) and $(\pi ,\pi )$. Hence area bounded by the two curves
$={\int }_0^{\pi }(x+sinx)dx-{\int }_0^{\pi }xdx={\int }_0^{\pi }sinxdx$
$=[-cosx{]}_0^{\pi }=-cos\pi +cos0=-(-1)+(1)=2$.