The area bounded by y=x|sinx|andx-axis between x=0,x=2π is
2π
3π
π
4π
Explanation for correct option
Finding the area of the region bounded by the curves
We will bifurcate the limit to (0,π)and(π,2π) for simple calculation
Required area:
=∫0πxsinxdx+∫π2πxsinxdx=-xcosx+sinx0π+-xcosx+sinxπ2π=(π+0)−(0+0)+(−2π+0)−(π+0)=π+3π=4π
Hence, option (D) is correct.