Check sibling questions

Ex 7.5, 10 - Integrate 2x - 3 / (x2 - 1) (2x + 3) - Integration by partial fraction - Type 3

Ex 7.5, 10 - Chapter 7 Class 12 Integrals - Part 2
Ex 7.5, 10 - Chapter 7 Class 12 Integrals - Part 3 Ex 7.5, 10 - Chapter 7 Class 12 Integrals - Part 4


Transcript

Ex 7.5, 10 2 3 2 1 2 + 3 We can write the integrand as 2 3 2 1 2 + 3 = 2 3 1 + 1 2 + 3 = + 1 + 1 + 2 + 3 = 1 2 + 3 + + 1 2 + 3 + 1 + 3 1 + 1 2 + 3 By cancelling denominator 2 3 = 1 2 +3 + +1 2 +3 + 1 +1 By substituting x = 1, in (1) 2 3 = 1 1 2+3 + 1+1 2+3 + 1+1 1 1 5 = 2 1 + 0+ 0 5 = 2 = 5 2 Similarly Putting x = 1, in (1) 2 3 = 1 1 2+3 + 1+1 2+3 + 1 1 1+1 1 = A 0 + 2 5 + 0 1 = 10 = 1 10 Similarly Putting x = 3 2 , in (1) 2 3 2 3 = 3 2 1 2 3 2 +3 + 3 2 +1 2 3 2 +3 + 3 2 1 3 2 +1 6 = 0+ 0+ 1 2 5 2 6 = 5 4 = 24 5 Therefore 2 3 + 1 1 2 + 3 = 5 2 + 1 + 1 10 1 + 24 5 2 + 3 Hence we can write it as 2 3 + 1 1 2 + 3 = 5 2 + 1 + 1 10 1 + 24 5 2 + 3 = 5 2 log +1 1 10 log 1 24 5 1 2 log 2 +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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.