Question 24 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

Evaluate: ∫_(-1)^1 log((2-x)/(2+x))dx

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Transcript

This is of the form ∫_(−𝑎)^𝑎▒𝑓(𝑥)𝑑𝑥 where 𝒇(𝒙)=𝐥𝐨𝐠((𝟐−𝒙)/(𝟐+𝒙)) And, 𝒇(−𝒙)=log((2 − (−𝑥))/(2 + (−𝑥))) 𝑓(−𝑥)=log((2 + 𝑥)/(2 − 𝑥)) Using log(𝑎/𝑏) = log a – log b 𝑓(−𝑥)=log⁡〖(2+𝑥)−log⁡(2−𝑥)〗 𝑓(−𝑥)=〖−(log〗⁡〖( 2−𝑥)−log⁡(2+𝑥)〗) 𝒇(−𝒙)=−𝐥𝐨𝐠((𝟐 − 𝒙)/(𝟐 + 𝒙)) Thus, 𝑓(−𝑥)=−𝑓(𝑥) ∴∫_(−1)^1 log((2 − 𝑥)/(2 + 𝑥))𝑑𝑥=0

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