`int_(-1)^(2) |x^(3)-x| dx` का मान ज्ञात कीजिए।

Explanation

यहाँ `[-1, 0]` पर `x^(3)-x ge 0` तथा `[0, 1]` पर `x^(3)-x le 0` तथा `[1,2]` पर `x^(3)-x ge 0` हो, तब
`int_(-1)^(2) |x^(3)-x|dx = int_(-1)^(0) (x^(3)-x) dx - int_(0)^(1) (x^(3)-x) dx + int_(1)^(2) (x^(3)-x) dx`
`=int_(-1)^(0) (x^(3)-x) dx+int_(0)^(1) (x-x^(3)) dx+int_(1)^(2) (x^(3)-x) dx`
`=[x^(4)/4-x^(2)/2]_(-1)^(0)+[x^(2)/2-x^(4)/4]_(0)^(1)+[x^(4)/4-x^(2)/2]_(1)^(2)`
`=0-(1/4-1/2)+(1/2-1/4)-0+ (16/4-4/2)-(1/4-1/2)`
`=-1/4+1/2+1/2-1/4 +4-2-1/4+1/2`
`=-3/4+3/2 +2`
`=-3/4+7/2=11^(pi)/4`