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▒𝑑𝑥/(√(5𝑥^2 − 2𝑥) ) ∫1▒𝑑𝑥/(√(5𝑥^2 − 2𝑥) ) = ∫1▒𝑑𝑥/(√(5(𝑥^2 − 2/5 𝑥) ) ) = ∫1▒𝑑𝑥/(√(5(𝑥^2 − 2(𝑥)(1/5)) ) ) = ∫1▒𝑑𝑥/(√(5(𝑥^2 − 2(𝑥)(1/5) + (1/5)^2− (1/5)^2 ) ) ) = ∫1▒𝑑𝑥/(√(5[(𝑥 − 1/5)^2−(1/5)^2 ] ) ) = ∫1▒𝑑𝑥/(√5 √((𝑥 − 1/5)^2−(1/5)^2 )) (Taking 5 common) [Adding and subtracting (1/5)^2] = ∫1▒𝑑𝑥/(√(5[(𝑥 − 1/5)^2−(1/5)^2 ] ) ) = ∫1▒𝑑𝑥/(√5 √((𝑥 − 1/5)^2−(1/5)^2 )) =1/√5 𝑙𝑜𝑔|𝑥−1/5+√((𝑥−1/5)^2−(1/5)^2 )|+𝐶 =1/√5 𝑙𝑜𝑔|𝑥−1/5+√(𝑥^2+(1/5)^2−2(𝑥)(1/5)−(1/5)^2 )|+𝐶 =𝟏/√𝟓 𝒍𝒐𝒈|𝒙−𝟏/𝟓+√(𝒙^𝟐−𝟐𝒙/𝟓)|+𝑪 It is of form ∫1▒〖𝑑𝑥/(√(𝑥^2 − 𝑎^2 ) )=𝑙𝑜𝑔|𝑥+√(𝑥^2−𝑎^2 )|+𝐶1〗 Replacing 𝑥 by (𝑥−1/5)𝑎𝑛𝑑 𝑎 𝑏𝑦 1/5, (Using√(𝑎.𝑏)=√𝑎 √𝑏)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.