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Chapter 7 Class 12 Integrals
Serial order wise

Example 40 - Chapter 7 Class 12 Integrals

Last updated at Dec. 16, 2024 by

Example 40 - Integral sin 2x cos 2x / root (9 - cos4 2x) - Examples

part 2 - Example 40 - Examples - Serial order wise - Chapter 7 Class 12 Integrals

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Example 40 Evaluate ∫1β–’(sin⁑〖2π‘₯ cos⁑2π‘₯ γ€— 𝑑π‘₯)/(√(9 βˆ’cos^4⁑(2π‘₯) ) ) 𝑑π‘₯ ∫1β–’(sin⁑〖2π‘₯ cos⁑2π‘₯ γ€— 𝑑π‘₯)/(√(9 βˆ’ cos^4⁑2π‘₯ ) ) 𝑑π‘₯ Let cos^2⁑2π‘₯=𝑑 Differentiating both sides w.r.t.π‘₯ –2.2 cos⁑2π‘₯ sin⁑2π‘₯=𝑑𝑑/𝑑π‘₯ 𝑑π‘₯=𝑑𝑑/(–4 cos⁑2π‘₯ sin⁑2π‘₯ ) Hence, our equation becomes ∫1β–’(sin⁑〖2π‘₯ cos⁑2π‘₯ γ€— )/(√(9 βˆ’ cos^4⁑2π‘₯ ) ) 𝑑π‘₯ =∫1β–’γ€–sin⁑〖2π‘₯ cos⁑2π‘₯ γ€—/√(9 βˆ’ 𝑑^2 ) 𝑑π‘₯γ€— =∫1β–’γ€–(sin⁑2π‘₯ cos⁑2π‘₯)/√(9 βˆ’ 𝑑^2 ) Γ— 𝑑𝑑/(–4 cos⁑2π‘₯ sin⁑2π‘₯ )γ€— =1/(βˆ’4) ∫1▒𝑑𝑑/√((3)^2 βˆ’ (𝑑)^2 ) =(βˆ’1)/( 4) [sin^(βˆ’1)⁑〖𝑑/3+𝐢1γ€— ] =(βˆ’1)/( 4) 𝑠𝑖𝑛^(βˆ’1) 𝑑/3βˆ’πΆ1/4 =(βˆ’πŸ)/( πŸ’) π’”π’Šπ’^(βˆ’πŸ) [𝟏/πŸ‘ 𝒄𝒐𝒔^𝟐 πŸπ’™]+π‘ͺ

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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