Example 9 - Find integrals (i) dx / x2 - 6x + 13 - Class 12

Example 9 - Chapter 7 Class 12 Integrals - Part 2

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  1. Chapter 7 Class 12 Integrals (Term 2)
  2. Serial order wise

Transcript

Example 9 Find the following integrals: (i) ∫1▒𝑑π‘₯/(π‘₯^2βˆ’ 6π‘₯ + 13) ∫1▒𝑑π‘₯/(π‘₯^2βˆ’ 6π‘₯ + 13) =∫1▒𝑑π‘₯/(π‘₯^2βˆ’ 2 Γ— 3 Γ— π‘₯ + 13) = ∫1▒𝑑π‘₯/((π‘₯^2 βˆ’ 2 . 3 π‘₯ + 3^2 ) + 13 βˆ’ 3^2 ) = ∫1▒𝑑π‘₯/((π‘₯ βˆ’ 3)^2 + 13 βˆ’ 9) = ∫1▒𝑑π‘₯/((π‘₯ βˆ’ 3)^2 + 4) = ∫1▒𝑑π‘₯/((π‘₯ βˆ’ 3)^2 + 2^2 ) ("Adding and subtracting " (3)^2 ) ("Using " π‘Ž^2βˆ’2π‘Žπ‘+𝑏^2=(π‘Žβˆ’π‘)^2 ) It is of form 𝑑π‘₯/(π‘₯^2 + π‘Ž^2 )=1/π‘Ž γ€–π‘‘π‘Žπ‘›γ€—^(βˆ’1)⁑〖π‘₯/π‘Žγ€—+𝐢 Replacing π‘₯ with (π‘₯βˆ’3) and π‘Ž with 2 =𝟏/𝟐 〖𝒕𝒂𝒏〗^(βˆ’πŸ)⁑〖(𝒙 βˆ’ πŸ‘)/πŸγ€— +π‘ͺ

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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.