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Prove that: int_(-a)^(a) log ((2-x)/(2+x)) dx=0 |
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Answer» SOLUTION :`"Let " f(x) =log ((2-x)/(2+x))` `RARR ""f(-x) =log ((2+x)/(2-x))` `=-log ((2-x)/(2+x))=-f(x)` `rArr ` f(x) is an ODD FUNCTION . `rArr ""int_(-a)^(a) f(x) dx=0` `rArr int_(-1)^(1) log ((2-x)/(2+x)) dx=0` HENCE Proved |
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