Example 4 - Find anti derivative F of f(x) = 4x3 - 6, f(0) = 3 - Using Formulaes

Examples 4 (last slide).jpg

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

Transcript

Example 4 Find the anti derivative F of f defined by ๐‘“(๐‘ฅ)=ใ€–4๐‘ฅใ€—^3โˆ’6, Where F (0) = 3 ๐‘“(๐‘ฅ)=4๐‘ฅ^3โˆ’6 Some F is Anti derivative F(๐‘ฅ)=โˆซ1โ–’๐‘“(๐‘ฅ)๐‘‘๐‘ฅ =โˆซ1โ–’(4๐‘ฅ^3โˆ’6)๐‘‘๐‘ฅ =โˆซ1โ–’ใ€–4๐‘ฅ^3 ๐‘‘๐‘ฅโˆ’6๐‘‘๐‘ฅใ€— =โˆซ1โ–’ใ€–4๐‘ฅ^3 ๐‘‘๐‘ฅใ€—โˆ’โˆซ1โ–’6๐‘‘๐‘ฅ =4โˆซ1โ–’ใ€–๐‘ฅ^3 ๐‘‘๐‘ฅใ€—โˆ’6โˆซ1โ–’ใ€–1.๐‘‘๐‘ฅใ€— =4โˆซ1โ–’ใ€–๐‘ฅ^3 ๐‘‘๐‘ฅใ€—โˆ’6โˆซ1โ–’ใ€–๐‘ฅ^0 ๐‘‘๐‘ฅใ€— =(4 . ((๐‘ฅ^(3 + 1) )/(3 + 1))+๐ถ1)โˆ’(6(๐‘ฅ^(0 + 1)/(0 + 1))โˆ’๐ถ2) =(4 . ((๐‘ฅ^4 )/4)+๐ถ1)โˆ’(6(๐‘ฅ^1/1)โˆ’๐ถ2) =๐‘ฅ^4+๐ถ1โˆ’6๐‘ฅโˆ’๐ถ2 =๐‘ฅ^4โˆ’6๐‘ฅ+(๐ถ1โˆ’๐ถ2) =๐‘ฅ^4โˆ’6๐‘ฅ+๐ถ So, F(๐‘ฅ)=๐‘ฅ^4โˆ’6๐‘ฅ+๐ถ Given F(0)=3 So, F(๐‘ฅ)=๐‘ฅ^4โˆ’6๐‘ฅ+๐ถ 3=0+0+๐ถ" " "C = 3" So, F(๐’™)=๐’™^๐Ÿ’โˆ’๐Ÿ”๐’™+๐Ÿ‘

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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.