Example 9 (iii) - Chapter 7 Class 12 Integrals
Last updated at April 16, 2024 by Teachoo
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Question 3 (Supplementary NCERT) Important Deleted for CBSE Board 2024 Exams
Chapter 7 Class 12 Integrals
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Transcript
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)
