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Example 3 - Chapter 7 Class 12 Integrals - Part 3

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Example 3 Find the following integrals: (iii) ∫▒(1 − sin⁡𝑥)/cos^2⁡𝑥 𝑑𝑥 ∫▒(1 − sin⁡𝑥)/cos^2⁡𝑥 𝑑𝑥 = ∫▒(1/cos^2⁡𝑥 − sin⁡𝑥/cos^2⁡𝑥 ) 𝑑𝑥 = ∫▒(sec^2⁡𝑥−sin⁡𝑥/𝑐𝑜𝑠⁡𝑥 . 1/𝑐𝑜𝑠⁡𝑥 ) 𝑑𝑥 = ∫▒(sec^2⁡𝑥−tan⁡𝑥 sec⁡𝑥 ) 𝑑𝑥 = 𝒕𝒂𝒏⁡𝒙−𝒔𝒆𝒄⁡𝒙+𝑪 As ∫1▒〖𝑠𝑒𝑐^2 𝑥 𝑑𝑥〗=tan⁡𝑥+𝐶 ∫1▒〖𝑠𝑒𝑐 𝑥 tan⁡〖𝑥 𝑑𝑥〗 〗=𝑠𝑒𝑐 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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.