# Ex 7.10, 1 - Chapter 7 Class 12 Integrals (Term 2)

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 7.10, 1 Evaluate the integrals using substitution 01 𝑥 𝑥2 + 1𝑑𝑥 𝑥 𝑥2+1 𝑑𝑥 Put 𝑡= 𝑥2+1 Differentiating w.r.t.𝑥 𝑑𝑡𝑑𝑥= 𝑑𝑑𝑥 𝑥2+1 𝑑𝑡𝑑𝑥=2𝑥 𝑑𝑡2𝑥=𝑑𝑥 Hence when 𝑥 varies from 0 to 1 then 𝑡 varies from 1 to 2 Therefore 01 𝑥 𝑥2+1𝑑𝑥= 12 𝑥𝑡 𝑑𝑡2𝑥 = 12 12 𝑑𝑡𝑡 = 12 𝑙𝑜𝑔 𝑡12 = 12 𝑙𝑜𝑔 2−𝑙𝑜𝑔 1 = 12 𝑙𝑜𝑔 2−0 = 12𝑙𝑜𝑔 2 = 𝟏𝟐𝒍𝒐𝒈 𝟐

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.