Integration Full Chapter Explained - Integration Class 12 - Everything you need

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
Misc 2 Important
Misc 3 Important
Misc 4
Misc 5 Important
Misc 6
Misc 7 Important
Misc 8 Important
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Misc 10 Important
Misc 11
Misc 12
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Misc 14 Important
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Misc 18 Important
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Misc 24 Important
Misc 25 Important
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Misc 30 Important
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Misc 33 Important
Misc 34
Misc 35 You are here
Misc 36
Misc 37
Misc 38 Important
Misc 39
Misc 40 Important Not in Syllabus - CBSE Exams 2021
Misc 41 Important
Misc 42
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Misc 44 Important
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