What is `int_(-1)^(1) x|x| dx`equal to ?

Options

A. `2`
B. `1`
C. `0`
D. `-1`

Answer

C

Explanation

Let `I = int_(-1)^(1)x|x|dx= int_(-1)^(0) x(-x)dx+ int_(0)^(1)x(x) dx`
`( :' |x| = {{:(x " if " x ge 0),(-x" if " x lt 0):})`
`= -int_(-1)^(0) dx + int_(0)^(1) x^(2) dx`
`= (-x^(3))/(3)"|"_(-1)^(0) +(x^(3))/(3)"|"_(0)^(1) =- (0+1/3) + 1/3 = 0`