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Evaluate ∫2−2 x2/(1+5x) dx - Mathematics

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Evaluate `int_(-2)^2x^2/(1+5^x)dx`

 
 
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Solution

 

 Consider the given integral

`I= int_(-2)^2x^2/(1+5^x)dx`

Let us use the property,

`int_a^bf(x)dx=int_b^af(a+b-x)dx`

`:.I = int_(-2)^2(-x)^2/(1+5^(-x))dx`

 `=int_(-2)^2(5^(x)x^2)/(1+5^x)dx `

 Adding equations (1) and (2), we have,

`2I=int_(-2)^2(1+5^x)/(1+5^x)xx x^2dx`

`=int_(-2)^2x^2dx`

`=[x^3/3]^2`

`=1/3[8-(8)]`

`=1/3[16]`

`=>I= 8/3`

 

 
Concept: Properties of Definite Integrals
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