Question

The area of the region bounded by the curve $y=x\sin x$ and $X$-axis between $x=0,x=2\pi$ is

• A. $4\pi$ sq. units
• B. $2\pi$ sq. units
• C. $\frac{\pi }{3}$ sq. units
• D. $\frac{\pi }{4}$ sq. units

Answer 1

The correct option is A $4\pi$ sq. units

${\int }_0^{2\pi }\left(xsinx\right).dx$.
By Applying ILATE rule, we get
$[-xcosx+sin(x){]}_0^{2\pi }$.
$=4\pi$