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Example 32 - Evaluate integral  x sin x / 1 + cos2 x dx - Definate Integration by properties - P4

Example 32 - Chapter 7 Class 12 Integrals - Part 2
Example 32 - Chapter 7 Class 12 Integrals - Part 3
Example 32 - Chapter 7 Class 12 Integrals - Part 4

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Transcript

Example 32 Evaluate ∫_0^πœ‹β–’(π‘₯ 𝑠𝑖𝑛 π‘₯)/(1 + cos^2⁑π‘₯ ) 𝑑π‘₯ =(βˆ’πœ‹)/2 [tan^(βˆ’1)⁑(𝑑) ]_0^πœ‹ Putting t = cos x =(βˆ’πœ‹)/2 [tan^(βˆ’1)⁑(cos⁑π‘₯ ) ]_0^πœ‹ =(βˆ’πœ‹)/2 [tan^(βˆ’1)⁑〖[cosβ‘πœ‹ ]βˆ’tan^(βˆ’1)⁑[cos⁑0 ] γ€— ] =(βˆ’πœ‹)/2 [tan^(βˆ’1)⁑〖(βˆ’1)βˆ’tan^(βˆ’1)⁑(1) γ€— ] =(βˆ’πœ‹)/2 [βˆ’tan^(βˆ’1)⁑〖(1)βˆ’tan^(βˆ’1)⁑(1) γ€— ] =(βˆ’πœ‹)/2 [βˆ’2 tan^(βˆ’1)⁑(1) ] =πœ‹[tan^(βˆ’1)⁑(1) ] = πœ‹[πœ‹/4] =𝝅^𝟐/πŸ’

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.