Question

The area bounded by the curve $y=\sin x$ between $x=0$ and $x=2\pi$ given by

• A. $4sq.units$
• B. $3sq.units$
• C. $0sq.units$
• D. $2sq.units$

Answer 1

Answer: (A)

We have, $y=\sin x,x=0$ and $x=2\pi$
$\therefore$ Required area = Area of shaded region
$\underset{0}{\overset{2\pi }{\int }}\left|\sin x\right|dx=\underset{0}{\overset{\pi }{\int }}\sin xdx+\underset{\pi }{\overset{2\pi }{\int }}\left(-\sin x\right)dx$
$=-{\left[\cos x\right]}_0^{\pi }+{\left[\cos x\right]}_{\pi }^{2\pi }$
$=-\left[\cos \pi -\cos 0\right]+\left[\cos 2\pi -\cos \pi \right]$
$=-\left[-1-1\right]+\left[1+1\right]=4$