Example 12 - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 12 Find 𝑥2+ 1 𝑥2 − 5𝑥 + 6 𝑑𝑥 Solving Integrand 𝑥2+ 1 𝑥2 − 5𝑥 + 6 𝑥2+ 1 𝑥2 − 5𝑥 + 6= 𝑥2+ 1 − 5𝑥 + 6 + 5𝑥 − 6 𝑥2 − 5𝑥 + 6 = 𝑥2 − 5𝑥 + 6 + 5𝑥 − 5 𝑥2 − 5𝑥 + 6 = 𝑥2 − 5𝑥 + 6 𝑥2 − 5𝑥 + 6 + 5𝑥 − 5 𝑥2 − 5𝑥 + 6 =1+ 5𝑥 − 5 𝑥2 − 5𝑥 + 6 =1+ 5𝑥 − 5 𝑥2 − 2𝑥 − 3𝑥 + 6 =1+ 5𝑥 − 5𝑥 𝑥 − 2 −3 𝑥 − 2 =1+ 5𝑥 − 5 𝑥 − 2 𝑥 − 3 Now solving 5𝑥 − 5 𝑥 − 2 𝑥 − 3 using partial fractions Let 5 𝑥 − 1 𝑥 − 2 𝑥 − 3= 𝐴 𝑥 − 2 + 𝐵 𝑥 − 3 5 𝑥 − 1 𝑥 − 2 𝑥 − 3= 𝐴 𝑥 − 3 + 𝐵 𝑥 − 2 𝑥 − 2 𝑥 − 3 ⇒5 𝑥−1=𝐴 𝑥−3+𝐵 𝑥−2 Hence we can write it as 5 𝑥 − 1 𝑥 − 2 𝑥 − 3 = 𝐴 𝑥 − 2 + 𝐵 𝑥 − 3 Now, 𝑥2+ 1 𝑥2 − 5𝑥 + 6 𝑑𝑥= 1+ 5 𝑥 − 1 𝑥 − 2 𝑥 − 3 𝑑𝑥 = 1+ −5 𝑥 − 2 + 10 𝑥 − 3 𝑑𝑥 = 1𝑑𝑥− −5 𝑥 − 2 𝑑𝑥+ 10 𝑥 − 3 𝑑𝑥 =𝒙−𝟓 𝒍𝒐𝒈 𝒙−𝟐+𝟏𝟎 𝒍𝒐𝒈 𝒙−𝟑+𝐂
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About the Author
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