`int_(-2)^(2) (3x^(2))/((1+e^(x))) dx` का मान कीजिए।

Explanation

माना `I=int_(-2)^(2) (3x^(2))/(1+e^(x)) dx`
`:' int_(a)^(b) f(x)dx = int_(a)^(b) f(a+b-x) dx` के सूत्रानुसार
`I=int_(-2)^(2) (3x^(2))/(1+e^(x)) dx=int_(-2)^(2) (3x^(2) e^(x))/(e^(x)+1) dx`
`:. 2I=int_(0)^(2) [(3x^(2))/(1+e^(x))+(3x^(2)e^(x))/(e^(x)+1)] dx`
`=int_(0)^(2) 3x^(2) [1/(1+e^(x))+e^(x)/(e^(x)+1)] dx`
`=int_(0)^(2) 3x^(2) ((1+e^(x))/(1+e^(x))) dx`
`=int_(0)^(2) 3x^(2) dx`
`=[(3x^(3))/3]_(0)^(2)=[x^(3)]_(0)^(2)`
`=(2)^(3)-(0)^(3)`
`=8`.