Example 9 - Chapter 7 Class 12 Integrals - Part 7

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Example 9 - Chapter 7 Class 12 Integrals - Part 8

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

Transcript

Example 9 Find the following integrals: (iii) ∫1▒𝑑π‘₯/(√(5π‘₯^2 βˆ’ 2π‘₯) ) ∫1▒𝑑π‘₯/(√(5π‘₯^2 βˆ’ 2π‘₯) ) = ∫1▒𝑑π‘₯/(√(5(π‘₯^2 βˆ’ 2/5 π‘₯) ) ) = ∫1▒𝑑π‘₯/(√(5(π‘₯^2 βˆ’ 2(π‘₯)(1/5)) ) ) = ∫1▒𝑑π‘₯/(√(5(π‘₯^2 βˆ’ 2(π‘₯)(1/5) + (1/5)^2βˆ’ (1/5)^2 ) ) ) = ∫1▒𝑑π‘₯/(√(5[(π‘₯ βˆ’ 1/5)^2βˆ’(1/5)^2 ] ) ) = ∫1▒𝑑π‘₯/(√5 √((π‘₯ βˆ’ 1/5)^2βˆ’(1/5)^2 )) (Taking 5 common) [Adding and subtracting (1/5)^2] = ∫1▒𝑑π‘₯/(√(5[(π‘₯ βˆ’ 1/5)^2βˆ’(1/5)^2 ] ) ) = ∫1▒𝑑π‘₯/(√5 √((π‘₯ βˆ’ 1/5)^2βˆ’(1/5)^2 )) =1/√5 π‘™π‘œπ‘”|π‘₯βˆ’1/5+√((π‘₯βˆ’1/5)^2βˆ’(1/5)^2 )|+𝐢 =1/√5 π‘™π‘œπ‘”|π‘₯βˆ’1/5+√(π‘₯^2+(1/5)^2βˆ’2(π‘₯)(1/5)βˆ’(1/5)^2 )|+𝐢 =𝟏/βˆšπŸ“ π’π’π’ˆ|π’™βˆ’πŸ/πŸ“+√(𝒙^πŸβˆ’πŸπ’™/πŸ“)|+π‘ͺ It is of form ∫1▒〖𝑑π‘₯/(√(π‘₯^2 βˆ’ π‘Ž^2 ) )=π‘™π‘œπ‘”|π‘₯+√(π‘₯^2βˆ’π‘Ž^2 )|+𝐢1γ€— Replacing π‘₯ by (π‘₯βˆ’1/5)π‘Žπ‘›π‘‘ π‘Ž 𝑏𝑦 1/5, (Using√(π‘Ž.𝑏)=βˆšπ‘Ž βˆšπ‘)

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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.