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Question
Evaluate the following using properties of definite integral:
`int_(-1)^1 log ((2 - x)/(2 + x)) "d"x`
Sum
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Solution
Let f(x = `log (2 - x)/(2 + x))`
f(– x) = `log ((2 - (- x))/(2 + (– x)))`
= `log ((2 + x)/(2 - x))`
= `log ((2 - x)/(2 + x))^-1`
= `- log ((2 - x)/(2 + x))`
⇒ (fx) = – f(x)
∴ f(x) is an odd function
∴ `int_(-1)^1 log ((2 - x)/(2 + x)) "d"x` = 0
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