Example 24 - Chapter 7 Class 12 Integrals

Last updated at December 16, 2024 by

Example 24 - Find integral root 3 - 2x - x^2 dx - Teachoo

Example 24 - Chapter 7 Class 12 Integrals - Part 2

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Example 24 Find ∫1▒√(3−2𝑥−𝑥^2 ) 𝑑𝑥 ∫1▒〖√(3−2𝑥−𝑥^2 ) 𝑑𝑥〗 =∫1▒√(3−(2𝑥+𝑥^2 ) ) 𝑑𝑥 Adding and Subtracting 1^2 =∫1▒√(3−(𝑥^2+2𝑥+1^2−1^2 ) ) 𝑑𝑥 =∫1▒√(3−(𝑥^2+2𝑥+1^2 )+1) 𝑑𝑥 =∫1▒√(3+1−(𝑥^2+2𝑥+1^2 ) ) 𝑑𝑥 =∫1▒√(4−(𝑥^2+2𝑥+1^2 ) ) 𝑑𝑥 =∫1▒√(2^2−(𝑥+1)^2 ) 𝑑𝑥 It is of the form ∫1▒〖√(𝑎^2−𝑥^2 ) 𝑑𝑥=1/2 𝑥√(𝑎^2−𝑥^2 )+𝑎^2/2 𝑠𝑖𝑛^(−1) 𝑥/𝑎+𝐶〗 Replacing a with 2 and 𝑥 with (𝑥+1) =1/2 (𝑥+1) √(2^2−(𝑥+1)^2 )+2^2/2 𝑠𝑖𝑛^(−1) ((𝑥 + 1))/2+𝐶 =1/2 (𝑥+1) √(4−(𝑥^2+1^2+2𝑥))+2𝑠𝑖𝑛^(−1) ((𝑥 + 1))/2+𝐶 =𝟏/𝟐 (𝒙+𝟏) √(𝟑−𝟐𝒙−𝒙^𝟐 )+𝟐 𝒔𝒊𝒏^(−𝟏) ((𝒙 + 𝟏))/𝟐+𝑪

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo