Evaluate: ∫_(-1)^1 log((2-x)/(2+x))dx
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CBSE Class 12 Sample Paper for 2024 Boards
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CBSE Class 12 Sample Paper for 2024 Boards
Last updated at April 16, 2024 by Teachoo
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This is of the form โซ_(โ๐)^๐โ๐(๐ฅ)๐๐ฅ where ๐(๐)=๐ฅ๐จ๐ ((๐โ๐)/(๐+๐)) And, ๐(โ๐)=log((2 โ (โ๐ฅ))/(2 + (โ๐ฅ))) ๐(โ๐ฅ)=log((2 + ๐ฅ)/(2 โ ๐ฅ)) Using log(๐/๐) = log a โ log b ๐(โ๐ฅ)=logโกใ(2+๐ฅ)โlogโก(2โ๐ฅ)ใ ๐(โ๐ฅ)=ใโ(logใโกใ( 2โ๐ฅ)โlogโก(2+๐ฅ)ใ) ๐(โ๐)=โ๐ฅ๐จ๐ ((๐ โ ๐)/(๐ + ๐)) Thus, ๐(โ๐ฅ)=โ๐(๐ฅ) โดโซ_(โ1)^1โlog((2 โ ๐ฅ)/(2 + ๐ฅ))๐๐ฅ=0