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