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Example 9 - Chapter 7 Class 12 Integrals - Part 7

Example 9 - Chapter 7 Class 12 Integrals - Part 8

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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.