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Example 4 - Chapter 7 Class 12 Integrals (Term 2)
Last updated at Dec. 24, 2018 by Teachoo
Transcript
Example 4 Find the anti derivative F of f defined by ๐(๐ฅ)=ใ4๐ฅใ^3โ6, Where F (0) = 3 ๐(๐ฅ)=4๐ฅ^3โ6 Some F is Anti derivative F(๐ฅ)=โซ1โ๐(๐ฅ)๐๐ฅ =โซ1โ(4๐ฅ^3โ6)๐๐ฅ =โซ1โใ4๐ฅ^3 ๐๐ฅโ6๐๐ฅใ =โซ1โใ4๐ฅ^3 ๐๐ฅใโโซ1โ6๐๐ฅ =4โซ1โใ๐ฅ^3 ๐๐ฅใโ6โซ1โใ1.๐๐ฅใ =4โซ1โใ๐ฅ^3 ๐๐ฅใโ6โซ1โใ๐ฅ^0 ๐๐ฅใ =(4 . ((๐ฅ^(3 + 1) )/(3 + 1))+๐ถ1)โ(6(๐ฅ^(0 + 1)/(0 + 1))โ๐ถ2) =(4 . ((๐ฅ^4 )/4)+๐ถ1)โ(6(๐ฅ^1/1)โ๐ถ2) =๐ฅ^4+๐ถ1โ6๐ฅโ๐ถ2 =๐ฅ^4โ6๐ฅ+(๐ถ1โ๐ถ2) =๐ฅ^4โ6๐ฅ+๐ถ So, F(๐ฅ)=๐ฅ^4โ6๐ฅ+๐ถ Given F(0)=3 So, F(๐ฅ)=๐ฅ^4โ6๐ฅ+๐ถ 3=0+0+๐ถ" " "C = 3" So, F(๐)=๐^๐โ๐๐+๐
Examples
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Example 1 (ii)
Example 1 (iii)
Example 2 (i)
Example 2 (ii)
Example 2 (iii) Important
Example 3 (i)
Example 3 (ii) Important
Example 3 (iii)
Example 4 You are here
Example 5 (i)
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Example 5 (iii) Important
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Example 25 Important Deleted for CBSE Board 2022 Exams
Example 26 Deleted for CBSE Board 2022 Exams
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Example 25 (Supplementary NCERT) Important Deleted for CBSE Board 2022 Exams
About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.