Example 3 - Chapter 7 Class 12 Integrals
Last updated at Dec. 20, 2019 by Teachoo
Transcript
Example 3 Find the following integrals: (i) ∫▒(sinx+cosx ) dx ∫▒(sin𝑥+cos𝑥 ) 𝑑𝑥 =∫1▒(sin𝑥 ) 𝑑𝑥+∫1▒〖〖(cos〗𝑥) 〗 𝑑𝑥 =−𝐜𝐨𝐬𝒙+𝐬𝐢𝐧𝒙+𝑪 As ∫1▒(sin𝑥 ) 𝑑𝑥=−cos𝑥+𝐶 ∫1▒〖〖(cos〗𝑥) 〗 𝑑𝑥=sin𝑥+𝐶 Example 3 Find the following integrals: (ii) ∫▒〖𝑐𝑜𝑠𝑒𝑐 𝑥(𝑐𝑜𝑠𝑒𝑐 𝑥+cot𝑥 ) 〗 𝑑𝑥 ∫▒〖𝑐𝑜𝑠𝑒𝑐 𝑥(𝑐𝑜𝑠𝑒𝑐 𝑥+cot𝑥 ) 〗 𝑑𝑥 = ∫▒(𝑐𝑜𝑠𝑒𝑐 𝑥+𝑐𝑜𝑠𝑒𝑐 𝑥 cot𝑥 ) 𝑑𝑥 = ∫▒〖𝑐𝑜𝑠𝑒𝑐^2 𝑥 𝑑𝑥〗+∫▒〖𝑐𝑜𝑠𝑒𝑐 𝑥 cot𝑥 〗 𝑑𝑥 = −𝐜𝐨𝐭𝒙 −𝒄𝒐𝒔𝒆𝒄 𝒙+𝑪 As ∫1▒〖𝑐𝑜𝑠𝑒𝑐^2 𝑥〗 𝑑𝑥=−cot𝑥+𝐶 ∫1▒〖𝑐𝑜𝑠𝑒𝑐 𝑥 cot𝑥 𝑑𝑥〗=−𝑐𝑜𝑠𝑒𝑐 𝑥+𝐶 Example 3 Find the following integrals: (iii) ∫▒(1 − sin𝑥)/cos^2𝑥 𝑑𝑥 ∫▒(1 − sin𝑥)/cos^2𝑥 𝑑𝑥 = ∫▒(1/cos^2𝑥 − sin𝑥/cos^2𝑥 ) 𝑑𝑥 = ∫▒(sec^2𝑥−sin𝑥/𝑐𝑜𝑠𝑥 . 1/𝑐𝑜𝑠𝑥 ) 𝑑𝑥 = ∫▒(sec^2𝑥−tan𝑥 sec𝑥 ) 𝑑𝑥 = 𝒕𝒂𝒏𝒙−𝒔𝒆𝒄𝒙+𝑪 As ∫1▒〖𝑠𝑒𝑐^2 𝑥 𝑑𝑥〗=tan𝑥+𝐶 ∫1▒〖𝑠𝑒𝑐 𝑥 tan〖𝑥 𝑑𝑥〗 〗=𝑠𝑒𝑐 𝑥+𝐶
Examples
Example 1
Example 2
Example 3 Important You are here
Example 4
Example 5
Example 6 Important
Example 7 Important
Example 8
Example 9
Example 10 Important
Example 11
Example 12
Example 13 Important
Example 14
Example 15 Important
Example 16 Important
Example 17
Example 18 Important
Example 19
Example 20 Important
Example 21 Important
Example 22 Important
Example 23
Example 24
Example 25 Important
Example 26
Example 27 Important
Example 28
Example 29
Example 30 Important
Example 31
Example 32
Example 33
Example 34 Important
Example 35 Important
Example 36 Important
Example 37
Example 38 Important
Example 39 Important
Example 40 Important
Example 41 Important
Example 42 Important
Example 43 Important
Example 44 Important
Example 25 (Supplementary NCERT) Important
About the Author
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.