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 Dec. 13, 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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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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