Chapter 7 Class 12 Integrals
Concept wise

Misc 33 - Chapter 7 Class 12 Integrals

Last updated at December 16, 2024 by

Misc 33 - Prove definite integral 0->1 x ex dx = 1 - Miscellaneous - Miscellaneous

part 2 - Misc 33 - Miscellaneous - Serial order wise - Chapter 7 Class 12 Integrals

Take a fresh quiz. Then take another.
Every attempt is a new AI-adaptive Teachoo quiz with 5 questions, selected from your answers, mistakes, and progress.
Remove Ads Share on WhatsApp

Transcript

Misc 33 Prove that āˆ«_0^1ā–’š‘„ š‘’^š‘„ š‘‘š‘„=1 Solving L.H.S āˆ«_0^1ā–’š‘„ š‘’^š‘„ š‘‘š‘„ First we will solve āˆ«1ā–’š’™ š’†^š’™ š’…š’™ āˆ«1ā–’š‘„ š‘’^š‘„ š‘‘š‘„ āˆ«1ā–’š‘„ š‘’^š‘„ š‘‘š‘„=š‘„āˆ«1ā–’怖š‘’^š‘„ š‘‘š‘„怗āˆ’āˆ«1ā–’(š‘‘š‘„/š‘‘š‘„ āˆ«1ā–’怖š‘’^š‘„ š‘‘š‘„怗) š‘‘š‘„ = š‘„š‘’^š‘„āˆ’āˆ«1ā–’1. š‘’^š‘„ š‘‘š‘„ = š‘„š‘’^š‘„āˆ’š‘’^š‘„+š¶ Applying limits āˆ«1_0^1ā–’怖š‘„ š‘’^š‘„ š‘‘š‘„怗 = [š‘„š‘’^š‘„āˆ’š‘’^š‘„ ]_0^1 = (1š‘’^1āˆ’š‘’^1 )āˆ’(0.š‘’^0āˆ’š‘’^0) = (š‘’^1āˆ’š‘’^1 )āˆ’ (0 āˆ’ 1) = 1 = R.H.S Hence proved.

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

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