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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
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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.