Chapter 7 Class 12 Integrals

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Important Questions for exams Class 12

Ex 7.9, 8 - Chapter 7 Class 12 Integrals (Important Question)

Last updated at July 14, 2026 by

  Ex 7.9, 8 - Evaluate integral (1/x - 1/ 2x2) e2x dx - Ex 7.9 - Ex 7.9

part 2 - Ex 7.9, 8 - Ex 7.9 - Serial order wise - Chapter 7 Class 12 Integrals
part 3 - Ex 7.9, 8 - Ex 7.9 - Serial order wise - Chapter 7 Class 12 Integrals

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Transcript

Ex 7.9, 8 Evaluate the integrals using substitution āˆ«_1^(2 )ā–’怖 (1/š‘„ āˆ’1/(2š‘„^2 )) 怗 š‘’^2š‘„ š‘‘š‘„ Let š‘”=2š‘„ š‘‘š‘”/š‘‘š‘„=2 š‘‘š‘”/2=š‘‘š‘„ Thus, when x varies from 1 to 2, t varies from 2 to 4 Substituting, āˆ«_1^(2 )ā–’怖 (1/š‘„ āˆ’1/(2š‘„^2 )) 怗 š‘’^2š‘„ š‘‘š‘„ = āˆ«_2^4ā–’怖š‘’^š‘” (1/(š‘”/2)āˆ’1/(2怖 (š‘”/2)怗^2 )) 怗 š‘‘š‘”/2 =āˆ«_2^4ā–’怖š‘’^š‘” (2/š‘”āˆ’4/(2š‘”^2 )) 怗 š‘‘š‘”/2 =āˆ«_2^4ā–’怖š‘’^š‘” (1/š‘”āˆ’2/š‘”^2 ) 怗 š‘‘š‘” It is of the form āˆ«1ā–’怖š‘’^š‘„ [š‘“(š‘„)+š‘“^ā€² (š‘„)] 怗 š‘‘š‘„=š‘’^š‘„ š‘“(š‘„)+š¶ Where š‘“(š‘„)=1/š‘” š‘“^ā€² (š‘„)= (āˆ’1)/š‘”^2 Hence, our equation becomes āˆ«_2^4ā–’怖š‘’^š‘” (1/š‘”āˆ’2/š‘”^2 ) 怗 š‘‘š‘” = [š‘’^š‘”Ɨ1/š‘”]_2^4 = (š‘’^4/4āˆ’š‘’^2/2) = (š’†^šŸ (š’†^šŸ āˆ’ šŸ))/šŸ’

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