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Ex 7.7, 5 - Integrate root 1 - 4x - x2 - Chapter 7 NCERT - Integration by specific formulaes - Formula 8

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex7.7, 5 √(1βˆ’4π‘₯βˆ’π‘₯2) ∫1β–’γ€–βˆš(1βˆ’4π‘₯βˆ’π‘₯^2 ) .𝑑π‘₯γ€— =∫1β–’γ€–βˆš(1βˆ’(4π‘₯+π‘₯^2 ) ) .𝑑π‘₯γ€— =∫1β–’γ€–βˆš(1βˆ’(π‘₯^2+4π‘₯) ) .𝑑π‘₯γ€— =∫1β–’γ€–βˆš(1βˆ’(π‘₯^2+2.2.π‘₯) ) 𝑑π‘₯γ€— =∫1β–’γ€–βˆš(1βˆ’[π‘₯^2+2.2.π‘₯+(2)^2βˆ’(2)^2 ] ) 𝑑π‘₯γ€— =∫1β–’γ€–βˆš(1βˆ’[(π‘₯+2)^2βˆ’4] ) .𝑑π‘₯γ€— =∫1β–’γ€–βˆš(1βˆ’(π‘₯+2)^2+4 ) 𝑑π‘₯γ€— =∫1β–’γ€–βˆš(5βˆ’(π‘₯+2)^2 ) 𝑑π‘₯γ€— =∫1β–’γ€–βˆš((√5)^2βˆ’(π‘₯+2)^2 ) 𝑑π‘₯γ€— = ((π‘₯ + 2))/2 √((√5)^2βˆ’(π‘₯+2)^2 )+(√5)^2/2 sin^(βˆ’1)⁑((π‘₯ + 2)/√5)+𝐢 = ((π‘₯ + 2))/2 √(5βˆ’γ€–(π‘₯γ€—^2+4π‘₯+4))+ 5/2 γ€– sinγ€—^(βˆ’1)⁑((π‘₯ + 2)/√5)+𝐢 = ((π‘₯ + 2))/2 √(5βˆ’π‘₯^2βˆ’4π‘₯βˆ’4)+5/2 γ€– sinγ€—^(βˆ’1)⁑((π‘₯ + 2)/√5)+𝐢 = πŸ“/𝟐 γ€– π’”π’Šπ’γ€—^(βˆ’πŸ)⁑((𝒙 + 𝟐)/βˆšπŸ“)+((𝒙 + 𝟐))/𝟐 √(πŸβˆ’π’™^πŸβˆ’πŸ’π’™)+π‘ͺ

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