Integration Full Chapter Explained - https://you.tube/Integration-Class-12

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise

Transcript

Example 3 Find the following integrals: (i) ∫▒(sin⁡x+cos⁡x ) dx ∫▒(sin⁡𝑥+cos⁡𝑥 ) 𝑑𝑥 =∫1▒(sin⁡𝑥 ) 𝑑𝑥+∫1▒〖〖(cos〗⁡𝑥) 〗 𝑑𝑥 =−𝐜𝐨𝐬⁡𝒙+𝐬𝐢𝐧⁡𝒙+𝑪 As ∫1▒(sin⁡𝑥 ) 𝑑𝑥=−cos⁡𝑥+𝐶 ∫1▒〖〖(cos〗⁡𝑥) 〗 𝑑𝑥=sin⁡𝑥+𝐶 Example 3 Find the following integrals: (ii) ∫▒〖𝑐𝑜𝑠𝑒𝑐 𝑥(𝑐𝑜𝑠𝑒𝑐 𝑥+cot⁡𝑥 ) 〗 𝑑𝑥 ∫▒〖𝑐𝑜𝑠𝑒𝑐 𝑥(𝑐𝑜𝑠𝑒𝑐 𝑥+cot⁡𝑥 ) 〗 𝑑𝑥 = ∫▒(𝑐𝑜𝑠𝑒𝑐 𝑥+𝑐𝑜𝑠𝑒𝑐 𝑥 cot⁡𝑥 ) 𝑑𝑥 = ∫▒〖𝑐𝑜𝑠𝑒𝑐^2 𝑥 𝑑𝑥〗+∫▒〖𝑐𝑜𝑠𝑒𝑐 𝑥 cot⁡𝑥 〗 𝑑𝑥 = −𝐜𝐨𝐭⁡𝒙 −𝒄𝒐𝒔𝒆𝒄 𝒙+𝑪 As ∫1▒〖𝑐𝑜𝑠𝑒𝑐^2 𝑥〗 𝑑𝑥=−cot⁡𝑥+𝐶 ∫1▒〖𝑐𝑜𝑠𝑒𝑐 𝑥 cot⁡𝑥 𝑑𝑥〗=−𝑐𝑜𝑠𝑒𝑐 𝑥+𝐶 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
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.