Example 2 - Find integrals (i) x^3 - 1 / x^2 dx (ii) x^2/3 + 1 dx

Example 2 - Chapter 7 Class 12 Integrals - Part 2

 

  1. Chapter 7 Class 12 Integrals (Term 2)
  2. Serial order wise

Transcript

Example 2 Find the following integrals: (i) βˆ«β–’(π‘₯^3 βˆ’ 1)/π‘₯^2 𝑑π‘₯ ∫1β–’γ€–((π‘₯^3 βˆ’ 1))/π‘₯^2 .𝑑π‘₯γ€— =∫1β–’(π‘₯^3/π‘₯^2 βˆ’1/π‘₯^2 )𝑑π‘₯ =∫1β–’γ€–(π‘₯βˆ’1/π‘₯^2 ).𝑑π‘₯γ€— =∫1β–’γ€–π‘₯ 𝑑π‘₯βˆ’βˆ«1β–’γ€–1/π‘₯^2 𝑑π‘₯γ€—γ€— =∫1β–’γ€–π‘₯^1 𝑑π‘₯βˆ’βˆ«1β–’γ€–π‘₯^(βˆ’2). 𝑑π‘₯γ€—γ€— =[(π‘₯^(1 + 1)/(1 + 1))]βˆ’[(π‘₯^(βˆ’2 + 1)/(βˆ’2 + 1))]+𝐢 =π‘₯^2/2βˆ’π‘₯^(βˆ’1)/(βˆ’1)+𝐢 (β–ˆ(∫1β–’γ€–π‘₯^𝑛 𝑑π‘₯=π‘₯^(𝑛+1)/(𝑛+1)+𝐢〗)) =π‘₯^2/2+π‘₯^(βˆ’1)+𝐢 =𝒙^𝟐/𝟐+𝟏/𝒙 +π‘ͺ

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
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.