Question 18 (OR 1st Question) - CBSE Class 12 Sample Paper for 2020 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

Find ∫ (3 + 3 cos⁡x)/(x + sin⁡x ) dx

Find integral (3 + 3 cos⁡ x)/(x + sin⁡ x) dx - Teachoo - CBSE Class 12

Question 18 (OR 1st Question) - CBSE Class 12 Sample Paper for 2020 Boards - Part 2

Transcript

Question 18 (OR 1st Question) Find ∫1 (3 + 3 cos⁡𝑥)/(𝑥 + sin⁡𝑥 ) dx ∫1 (3 + 3 cos⁡𝑥)/(𝑥 + sin⁡𝑥 ) dx = ∫1 (3(1 + cos⁡𝑥))/(𝑥 + sin⁡𝑥 ) dx Let t = x + sin x dt = (1 + cos x) dx Putting t and dt in equation = ∫1 3/𝑡 dt = 3 × ∫1▒1/𝑡 dt = 3 × log⁡〖|𝑡|〗 + C Putting back t = (x + sin x) = 3 × 𝒍𝒐𝒈⁡〖|(𝒙+𝐬𝐢𝐧⁡𝒙)|〗 + C

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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