Example 24 - Find integral root 3 - 2x - x2 dx - Examples

Examples 24 last slide.jpg

  1. Chapter 7 Class 12 Integrals
  2. Serial order wise

Transcript

Example 24 Find ∫1β–’βˆš(3βˆ’2π‘₯βˆ’π‘₯^2 ) 𝑑π‘₯ ∫1β–’γ€–βˆš(3βˆ’2π‘₯βˆ’π‘₯^2 ) 𝑑π‘₯γ€— =∫1β–’βˆš(3βˆ’(2π‘₯βˆ’π‘₯^2 ) ) 𝑑π‘₯ Adding and Subtracting 1^2 =∫1β–’βˆš(3βˆ’(π‘₯^2+2π‘₯+1^2βˆ’1^2 ) ) 𝑑π‘₯ =∫1β–’βˆš(3βˆ’(π‘₯^2+2π‘₯+1^2 )+1) 𝑑π‘₯ =∫1β–’βˆš(3+1βˆ’(π‘₯^2+2π‘₯+1^2 ) ) 𝑑π‘₯ =∫1β–’βˆš(4βˆ’(π‘₯^2+2π‘₯+1^2 ) ) 𝑑π‘₯ =∫1β–’βˆš(2^2βˆ’(π‘₯+1)^2 ) 𝑑π‘₯ It is of the form ∫1β–’γ€–βˆš(π‘Ž^2βˆ’π‘₯^2 ) 𝑑π‘₯=1/2 π‘₯√(π‘Ž^2βˆ’π‘₯^2 )+π‘Ž^2/2 𝑠𝑖𝑛^(βˆ’1) π‘₯/π‘Ž+𝐢〗 Replacing a with 2 and π‘₯ with (π‘₯+1) =1/2 (π‘₯+1) √(2^2βˆ’(π‘₯+1)^2 )+2^2/2 𝑠𝑖𝑛^(βˆ’1) ((π‘₯ + 1))/2+𝐢 =1/2 (π‘₯+1) √(4βˆ’(π‘₯^2+1^2+2π‘₯))+2^2/2 𝑠𝑖𝑛^(βˆ’1) ((π‘₯ + 1))/2+𝐢 =𝟏/𝟐 (𝒙+𝟏) √(πŸ‘βˆ’πŸπ’™βˆ’π’™^𝟐 )+𝟐 π’”π’Šπ’^(βˆ’πŸ) ((𝒙 + 𝟏))/𝟐+π‘ͺ

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.