Misc 36 - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Misc 36 Prove that β«_0^(π/4)βγ2 tanγ^3β‘π₯ ππ₯=1βlogβ‘2 Solving L.H.S 2β«_0^(π/4)βγ tanγ^3β‘π₯ ππ₯ = 2β«_0^(π/4)βγ tan π₯ tanγ^2β‘π₯ ππ₯ = 2β«_0^(π/4)βγ tan π₯ (secγ^2β‘γπ₯β1)γ ππ₯ = 2β«_0^(π/4)βγ tan π₯ secγ^2β‘π₯ ππ₯β 2β«_0^(π/4)βtanβ‘γπ₯ ππ₯γ π°_π = 2β«_π^(π /π)βγ πππ§ π πππγ^πβ‘π π π Let t = tan x ππ‘/ππ₯ = γπ ππγ^2 x dt = γπ ππγ^2x dx Substituting, 2β«1_0^1βγπ‘ ππ‘γ = 2 [π‘^2/2]_0^1 = 2 (1/2β0) =1 π°_π= 2β«_π^(π /π)βπππβ‘γπ π πγ 2β«_π^(π /π)βπππβ‘γπ π πγ = 2 ["log" |secβ‘π₯ |]_0^(π/4) = 2 ("log" β2β0) = 2 (log 2^(1/2)) = 2 (1/2 "log " 2) = log 2 Hence, = πΌ_1βπΌ_2 = 1 β log 2 = 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
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
Misc 21
Misc 22
Misc 23 Important
Misc 24 Important
Misc 25 Important
Misc 26 Important
Misc 27 Important
Misc 28
Misc 29 Important
Misc 30 Important
Misc 31 Important
Misc 32
Misc 33
Misc 34
Misc 35
Misc 36 Important You are here
Misc 37
Misc 38 (MCQ) Important
Misc 39 (MCQ)
Misc 40 (MCQ)
Integration Formula Sheet Important
Question 1 Important
Question 2 Important
Question 3 Important
Question 4 (MCQ) Important
About the Author
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