Example 9 (i) - Chapter 7 Class 12 Integrals

Last updated at April 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

Made by

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

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular