Question

The value of the integral ∫(|x+1|+|x| )dx is

Answer 1

$\mathfrak{\huge{\red{\underline{\underline{answer:-}}}}}$

|x|x|x|x is equal to −1−1 when xx is negative. (Because when x<0,x<0

, |x|=−x|x|=−x so |x|x=−xx=−1|x|x=−xx=−1 )

and it is equal to +1+1 when xx is positive. (Because when x>0,x>0, 

|x|=x|x|=x so |x|x=xx=1|x|x=xx=1 )

So, integration of |x|/x ×dx from limits -1 to 1

i.e. ∫−11|x|xdx∫−11|x|xdx

can be split into two parts,

∫−10|x|xdx+∫01|x|xdx∫−10|x|xdx+∫01|x|xdx

=∫−10(−1)dx+∫