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 1 Write an anti derivative for each of the following functions using the method of inspection: (i) cosโก2๐‘ฅ We know that (๐‘ ๐‘–๐‘› ๐‘ฅ)^โ€ฒ=๐‘๐‘œ๐‘  ๐‘ฅ (๐‘ ๐‘–๐‘› 2๐‘ฅ)^โ€ฒ=๐‘๐‘œ๐‘  2๐‘ฅร— 2 (๐‘ ๐‘–๐‘› 2๐‘ฅ)^โ€ฒ=2๐‘๐‘œ๐‘  2๐‘ฅ (๐‘ ๐‘–๐‘› 2๐‘ฅ)^โ€ฒ/2=๐‘๐‘œ๐‘  2๐‘ฅ โˆด Anti Derivative of (cos 2x) is ๐Ÿ/๐Ÿ (๐’”๐’Š๐’ ๐Ÿ๐’™) Example 1 Write an anti derivative for each of the following functions using the method of inspection: (ii) 3๐‘ฅ^2+4๐‘ฅ^3 We know that Adding (1) and (2) (๐‘ฅ^3 )^โ€ฒ+(๐‘ฅ^4 )^โ€ฒ=3๐‘ฅ^2+4๐‘ฅ^3 Hence Anti derivative of is ๐’™^๐Ÿ‘+๐’™^๐Ÿ’ (๐‘ฅ^3 )^โ€ฒ=3๐‘ฅ^( 3โˆ’1) (๐‘ฅ^3 )^โ€ฒ=3๐‘ฅ^2 Also, (๐‘ฅ^4 )^โ€ฒ=4๐‘ฅ^( 4โˆ’1) (๐‘ฅ^4 )^โ€ฒ=4๐‘ฅ^3 Example 1 Write an anti derivative for each of the following functions using the method of inspection: (iii) 1/๐‘ฅ, ๐‘ฅโ‰ 0 We know that (logโก๐‘ฅ )^โ€ฒ=1/( ๐‘ฅ) Hence Anti derivative of is ๐Ÿ/๐’™

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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.