Example 9 (i) - Chapter 7 Class 12 Integrals

Last updated at Dec. 16, 2024 by Teachoo

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

Example 9 - Chapter 7 Class 12 Integrals - Part 2

Next: Example 9 (ii) Important → Go Ad-free

Transcript

Example 9 Find the following integrals: (i) ∫1▒𝑑𝑥/(𝑥^2− 6𝑥 + 13) ∫1▒𝑑𝑥/(𝑥^2− 6𝑥 + 13) =∫1▒𝑑𝑥/(𝑥^2− 2 × 3 × 𝑥 + 13) = ∫1▒𝑑𝑥/((𝑥^2 − 2 . 3 𝑥 + 3^2 ) + 13 − 3^2 ) = ∫1▒𝑑𝑥/((𝑥 − 3)^2 + 13 − 9) = ∫1▒𝑑𝑥/((𝑥 − 3)^2 + 4) = ∫1▒𝑑𝑥/((𝑥 − 3)^2 + 2^2 ) ("Adding and subtracting " (3)^2 ) ("Using " 𝑎^2−2𝑎𝑏+𝑏^2=(𝑎−𝑏)^2 ) It is of form 𝑑𝑥/(𝑥^2 + 𝑎^2 )=1/𝑎 〖𝑡𝑎𝑛〗^(−1)⁡〖𝑥/𝑎〗+𝐶 Replacing 𝑥 with (𝑥−3) and 𝑎 with 2 =𝟏/𝟐 〖𝒕𝒂𝒏〗^(−𝟏)⁡〖(𝒙 − 𝟑)/𝟐〗 +𝑪

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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