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Misc 43 - If f (a + b - x) = f(x), then  x f(x) dx is - Definate Integration by properties - P3

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Misc 43 Choose the correct answer If ๐‘“๏ท๐‘Ž+๐‘โˆ’๐‘ฅ๏ทฏ=๐‘“๏ท๐‘ฅ๏ทฏ, then ๏ท๐‘Ž๏ทฎ๐‘๏ทฎ๐‘ฅ ๐‘“๏ท๐‘ฅ๏ทฏ๏ทฏ๐‘‘๐‘ฅ is equal to (A) ๏ท๐‘Ž+๐‘๏ทฎ2๏ทฏ๏ท๐‘Ž๏ทฎ๐‘๏ทฎ ๐‘“๏ท๐‘โˆ’๐‘ฅ๏ทฏ๏ทฏ๐‘‘๐‘ฅ (B) ๏ท๐‘Ž+๐‘๏ทฎ2๏ทฏ๏ท๐‘Ž๏ทฎ๐‘๏ทฎ ๐‘“๏ท๐‘+๐‘ฅ๏ทฏ๏ทฏ๐‘‘๐‘ฅ (C) ๏ท๐‘ โˆ’๐‘Ž๏ทฎ2๏ทฏ๏ท๐‘Ž๏ทฎ๐‘๏ทฎ ๐‘“๏ท๐‘ฅ๏ทฏ๏ทฏ๐‘‘๐‘ฅ (D) ๏ท๐‘Ž+๐‘๏ทฎ2๏ทฏ๏ท๐‘Ž๏ทฎ๐‘๏ทฎ ๐‘“๏ท๐‘ฅ๏ทฏ๏ทฏ๐‘‘๐‘ฅ Let I=๏ท๐‘Ž๏ทฎ๐‘๏ทฎ๐‘ฅ ๐‘“๏ท๐‘ฅ๏ทฏ๏ทฏ๐‘‘๐‘ฅ โˆด I=๏ท๐‘Ž๏ทฎ๐‘๏ทฎ๏ท๐‘Ž+๐‘โˆ’๐‘ฅ๏ทฏ ๐‘“๏ท๐‘Ž+๐‘โˆ’๐‘ฅ๏ทฏ๏ทฏ๐‘‘๐‘ฅ I=๏ท๐‘Ž๏ทฎ๐‘๏ทฎ๏ท๐‘Ž+๐‘โˆ’๐‘ฅ๏ทฏ ๐‘“๏ท๐‘ฅ๏ทฏ๏ทฏ๐‘‘๐‘ฅ I=๏ท๐‘Ž๏ทฎ๐‘๏ทฎ๏ท๐‘Ž+๐‘๏ทฏ ๐‘“๏ท๐‘ฅ๏ทฏ๏ทฏ๐‘‘๐‘ฅโˆ’๏ท๐‘Ž๏ทฎ๐‘๏ทฎ๐‘ฅ ๐‘“๏ท๐‘ฅ๏ทฏ๏ทฏ๐‘‘๐‘ฅ Adding (1) and (2) i.e (1) + (2) I+I=๏ท๐‘Ž๏ทฎ๐‘๏ทฎ๐‘ฅ ๐‘“๏ท๐‘ฅ๏ทฏ๏ทฏ๐‘‘๐‘ฅ+๏ท๐‘Ž๏ทฎ๐‘๏ทฎ๏ท๐‘Ž+๐‘๏ทฏ ๐‘“๏ท๐‘ฅ๏ทฏ๏ทฏ๐‘‘๐‘ฅโˆ’๏ท๐‘Ž๏ทฎ๐‘๏ทฎ๐‘ฅ ๐‘“๏ท๐‘ฅ๏ทฏ๏ทฏ๐‘‘๐‘ฅ 2I=๏ท๐‘Ž๏ทฎ๐‘๏ทฎ๏ท๐‘Ž+๐‘๏ทฏ ๐‘“๏ท๐‘ฅ๏ทฏ๏ทฏ๐‘‘๐‘ฅ 2I=๏ท๐‘Ž+๐‘๏ทฏ๏ท๐‘Ž๏ทฎ๐‘๏ทฎ๐‘“๏ท๐‘ฅ๏ทฏ๏ทฏ๐‘‘๐‘ฅ โˆด I=๏ท๐‘Ž + ๐‘๏ทฎ2๏ทฏ ๏ท๐‘Ž๏ทฎ๐‘๏ทฎ๐‘“๏ท๐‘ฅ๏ทฏ๏ทฏ๐‘‘๐‘ฅ โˆด Option D is correct .

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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