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Ex 7.5

Ex 7.5, 1

Ex 7.5, 2

Ex 7.5, 3 Important

Ex 7.5, 4

Ex 7.5, 5 You are here

Ex 7.5, 6 Important

Ex 7.5, 7 Important

Ex 7.5, 8

Ex 7.5, 9 Important

Ex 7.5, 10

Ex 7.5, 11 Important

Ex 7.5, 12

Ex 7.5, 13 Important

Ex 7.5, 14 Important

Ex 7.5, 15

Ex 7.5, 16 Important

Ex 7.5, 17

Ex 7.5, 18 Important

Ex 7.5, 19

Ex 7.5, 20 Important

Ex 7.5, 21 Important

Ex 7.5, 22 (MCQ)

Ex 7.5, 23 (MCQ) Important

Last updated at May 29, 2018 by Teachoo

Ex 7.5, 5 2𝑥 𝑥2 + 3𝑥 + 2 Solving integrand 2𝑥 𝑥2 + 3𝑥 + 2 = 2𝑥 𝑥2 + 2𝑥 + 𝑥 + 2 = 2𝑥𝑥 𝑥 + 2 + 1 𝑥 + 2 = 2𝑥 𝑥 + 2 𝑥 + 1 We can write it as 2𝑥 𝑥 + 2 𝑥 + 1 = 𝐴 𝑥 + 2 + 𝐵 𝑥 + 1 2𝑥 𝑥 + 2 𝑥 + 1 = 𝐴 𝑥 + 1 + 𝐵 𝑥 + 2 𝑥 + 2 𝑥 + 1 Cancelling denominator 2𝑥 = 𝐴 𝑥+1+𝐵 𝑥+2 Putting x = −1, in (1) 2 −1 = 𝐴 −1+1 + 𝐵 −1+2 −2 = 𝐴×0+𝐵 1 𝐵 = −2 Similarly putting x = − 2 , in (1) 2 −2 = 𝐴 −2+1 + 𝐵 −2+2 −4 = 𝐴 −1+𝐵×0 −4 = −𝐴 𝐴 = 4 Hence we can write it as 2𝑥 𝑥 + 2 𝑥 + 1 = 4 𝑥 + 2 + −2 𝑥 + 1 = 4 𝑥 + 2 − 2 𝑥 + 1 Integrating 𝑤.𝑟.𝑡.𝑥. 2𝑥 𝑥 + 2 𝑥 + 1 𝑑𝑥 = 4 𝑥 + 2 − 2 𝑥 + 1𝑑𝑥 = 4 𝑑𝑥 𝑥 + 2−2 𝑑𝑥 𝑥 + 1 = 𝟒 𝐥𝐨𝐠 𝒙+𝟐−𝟐 𝐥𝐨𝐠 𝒙+𝟏 +𝑪