The area bounded y=xe|x| and line |x|=1,y=0 is
4squnits
6squnits
1squnits
2squnits
Explanation for correct option
Finding the area bounded by the two curves
Given, y=xe|x| and line |x|=1,y=0
Now,
|x|=1⇒x=±1
∴y=xe|x|=xe-x-1<x<0xex0≤x<1∵x=±1
Therefore, the limits will be (-1,0)and(0,1)
The required area is,
=∫-10xe-xdx+∫01xexdx=-xe-x-e-x-10+xex-ex01=0-1-e-e+e-e-0-1=2squnits
Hence, the correct answer is option (D).
Find the area bounded by the curve y=xx,x-axis and the ordinates x=1,x=-1.