`int_(-2)^(2)(x^(2))/(1+5^(x))dx` का मान ज्ञात कीजिए ।

Explanation

माना `I=int_(-2)^(2)(x^(2))/(1+5^(x))dx" …(1)"`
`=int_(-2)^(2)((2-2-x)^(2))/(1+5^(2-2-x))dx`
`" "[because int_(1)^(b)f(a+b-x)dx]`
`=int_(-2)^(2)(x^(2))/(1+5^(-x))dx`
`rArr" "I=int_(-2)^(2)(5^(x)x^(2))/(5^(x)+1)dx" ...(2)"`
समीकरण (1 ) व (2 ) को जोड़ने पर
`2I=int_(-2)^(2)((1+5^(x))/(5^(x)+1))x^(2)dx`
`rArr" "2I=2int_(0)^(2)x^(2)dx`
[`because x^(2)` सम है, अतः `int_(-2)^(2)x^(2)d2int_(0)^(2)x^(2)dx]`
`rArr" "I=[(x^(3))/(3)]_(0)^(2)=(1)/(3)(2^(3)-0)=(8)/(3)`