Integration Full Chapter Explained - https://you.tube/Integration-Class-12

Last updated at Dec. 23, 2019 by Teachoo

Transcript

Misc 35 Prove that โซ_0^1โ๐ฅ ๐^๐ฅ ๐๐ฅ=1 Solving L.H.S โซ_0^1โ๐ฅ ๐^๐ฅ ๐๐ฅ First we will solve โซ1โ๐ ๐^๐ ๐ ๐ โซ1โ๐ฅ ๐^๐ฅ ๐๐ฅ Now we know that โซ1โใ๐(๐ฅ) ๐โก(๐ฅ) ใ ๐๐ฅ=๐(๐ฅ) โซ1โ๐(๐ฅ) ๐๐ฅโโซ1โ(๐^โฒ (๐ฅ) โซ1โ๐(๐ฅ) ๐๐ฅ) ๐๐ฅ Putting value of f(x) = x and g(x) = ex โซ1โ๐ฅ ๐^๐ฅ ๐๐ฅ=๐ฅโซ1โใ๐^๐ฅ ๐๐ฅใโโซ1โ(๐๐ฅ/๐๐ฅ โซ1โใ๐^๐ฅ ๐๐ฅใ) ๐๐ฅ = ๐ฅ๐^๐ฅโโซ1โ1. ๐^๐ฅ ๐๐ฅ = ๐ฅ๐^๐ฅโ๐^๐ฅ+๐ถ Applying limits โซ1_0^1โใ๐ฅ ๐^๐ฅ ๐๐ฅใ = [๐ฅ๐^๐ฅโ๐^๐ฅ ]_0^1 = (1๐^1โ๐^1 )โ(0.๐^0โ๐^0) = (๐^1โ๐^1 )โ (0 โ 1) = 1 = R.H.S Hence proved.

Miscellaneous

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Misc 2 Important

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Misc 14 Important

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Misc 18 Important

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Misc 24 Important

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Misc 33 Important

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Misc 35 You are here

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Integration Formula Sheet - Chapter 7 Class 12 Formulas Important

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.