Ex 7.5, 3 - Integrate 3x - 1 / (x - 1) (x - 2) (x - 3) - Integration by partial fraction - Type 3

Ex 7.5, 3 - Chapter 7 Class 12 Integrals - Part 2
Ex 7.5, 3 - Chapter 7 Class 12 Integrals - Part 3

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Ex 7.5, 3 3 1 1 2 3 We can write the integrand as 3 1 1 2 3 = 1 + 2 + 3 = 2 3 + 1 3 + 1 2 1 2 3 By cancelling denominator 3 1 = 2 3 + 1 3 + 1 2 Putting =1 in (1) 3 1 = 1 2 1 3 + 1 1 1 3 + 1 1 1 2 2 = 1 2 + 0+ 0 2 = 2 = 1 Similarly putting =2 , in (1) 3 2 1 = 2 2 2 3 + 2 1 2 3 + 2 1 2 2 6 1 = 0+ 1 1 + 0 5 = = 5 Similarly putting x = 3 , in (1) 3 3 1 = 3 2 3 3 + 3 1 3 3 + 3 1 3 2 9 1 = 0+ 0+ 2 1 8 = 2 = 4 Hence we can write it as 3 1 1 2 3 = 1 1 + 5 2 + 4 3 = 1 1 5 1 2 +4 1 3 = + +

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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