Chapter 7 Class 12 Integrals

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Ex 7.2, 20 - Chapter 7 Class 12 Integrals (Important Question)

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Ex 7.2, 20 - Integrate (e^2x - e^-2x) / (e^2x + e^-2x) - Ex 7.2

Ex 7.2, 20 - Chapter 7 Class 12 Integrals - Part 2

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Ex 7.2, 20 Integrate the function (š‘’^2š‘„ āˆ’ š‘’^(āˆ’2š‘„))/(š‘’^2š‘„ + š‘’^(āˆ’2š‘„) ) Let š‘’^2š‘„ + š‘’^(āˆ’2š‘„)= š‘” Differentiating both sides š‘¤.š‘Ÿ.š‘”.š‘„ š‘’^2š‘„. š‘‘(2š‘„)/š‘‘š‘„ +š‘’^(āˆ’2š‘„) š‘‘(āˆ’2š‘„)/š‘‘š‘„= š‘‘š‘”/š‘‘š‘„ 怖2š‘’怗^2š‘„āˆ’怖2š‘’怗^(āˆ’2š‘„)= š‘‘š‘”/š‘‘š‘„ 2(š‘’^2š‘„āˆ’š‘’^(āˆ’2š‘„) )=š‘‘š‘”/š‘‘š‘„ " " š‘‘š‘„ = š‘‘š‘”/2(š‘’^2š‘„āˆ’ š‘’^(āˆ’2š‘„) ) Integrating the function āˆ«1ā–’怖" " (š‘’^2š‘„ āˆ’ š‘’^(āˆ’2š‘„))/(š‘’^2š‘„ + š‘’^(āˆ’2š‘„) )怗. š‘‘š‘„ Putting š‘’^2š‘„ + š‘’^(āˆ’2š‘„)=š‘” & š‘‘š‘„=š‘‘š‘”/2(š‘’^2š‘„āˆ’ š‘’^(āˆ’2š‘„) ) = āˆ«1ā–’怖" " (š‘’^2š‘„ āˆ’ š‘’^(āˆ’2š‘„))/š‘”怗. š‘‘š‘”/2(š‘’^2š‘„āˆ’ š‘’^(āˆ’2š‘„) ) = āˆ«1ā–’怖" " 1/2š‘”怗. š‘‘š‘” = 1/2 āˆ«1ā–’1/š‘”. š‘‘š‘” = 1/2 logā”怖 |š‘”|怗+š¶ = 1/2 logā”怖 |š‘’^2š‘„ + š‘’^(āˆ’2š‘„) |怗+š¶ = šŸ/šŸ š’š’š’ˆā”怖 (š’†^šŸš’™ + š’†^(āˆ’šŸš’™) )怗+š‘Ŗ (Using āˆ«1ā–’1/š‘„. š‘‘š‘„=š‘™š‘œš‘”ā”|š‘„| ) (Using š‘”=š‘’^2š‘„ + š‘’^(āˆ’2š‘„)) (āˆ“ š‘’^2š‘„+š‘’^(āˆ’2š‘„)>0 )

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