Integration Full Chapter Explained - Integration Class 12 - Everything you need

Last updated at May 29, 2018 by Teachoo

Transcript

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

Ex 7.5

Ex 7.5, 1

Ex 7.5, 2

Ex 7.5, 3

Ex 7.5, 4

Ex 7.5, 5 You are here

Ex 7.5, 6 Important

Ex 7.5, 7

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

Ex 7.5, 14

Ex 7.5, 15

Ex 7.5, 16

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

Ex 7.5, 23 Important

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.