Example 24 - Chapter 7 Class 12 Integrals

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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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