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 1
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Misc 2 Important

Misc 3 Important

Misc 4

Misc 5 Important

Misc 6

Misc 7 Important

Misc 8 Important

Misc 9

Misc 10 Important

Misc 11

Misc 12

Misc 13

Misc 14 Important

Misc 15

Misc 16

Misc 17

Misc 18 Important

Misc 19 Important

Misc 20 Important

Misc 21

Misc 22

Misc 23

Misc 24 Important

Misc 25 Important

Misc 26 Important

Misc 27 Important

Misc 28 Important

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Misc 30 Important

Misc 31 Important

Misc 32 Important

Misc 33 Important

Misc 34

Misc 35 You are here

Misc 36

Misc 37

Misc 38 Important

Misc 39

Misc 40 Important Deleted for CBSE Board 2021 Exams only

Misc 41 Important

Misc 42

Misc 43

Misc 44 Important

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 10 years. He provides courses for Maths and Science at Teachoo.