Misc 41 - Chapter 7 Class 12 Integrals

Last updated at March 11, 2017 by Teachoo

Misc 41 - Class 12 - Integration - dx/ ex + e-x is equal - Integration by substitution - e^x

Transcript

Misc 41 Choose the correct answer ∫▒dx/(e^x + e^(-x) ) is equal to (A) tan^(-1) (e^x )+C (B) tan^(-1)⁡〖(e^(-x) )+C〗 (C) log⁡(e^x-e^(-x) )+C (D) log⁡(e^x+e^(-x) )+C ∫▒dx/(e^x + e^(-x) ) = ∫▒dx/(e^x + 1/e^x ) = ∫1▒(e^x dx)/(e^2x + 1) Let e^x=t dt/dx=e^x dt = e^x dx Substituting, = ∫1▒dt/(t^2 +1) = 〖tan〗^(-1) (t)+ C Putting value of t = 〖tan〗^(-1) (e^x )+ C Hence, answer is (A).

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Misc 41 Important You are here

Concept wise →

Chapter 7 Class 12 Integrals

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Ex 7.1
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Ex 7.3
Ex 7.4
Ex 7.5
Ex 7.6
Ex 7.7
Ex 7.8
Ex 7.9
Ex 7.10
Ex 7.11
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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.