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Misc 39 - Prove that 0->1 sin-1 x dx = pi/2 - 1 - Definate Integration - By Formulae

Misc 39 - Chapter 7 Class 12 Integrals - Part 2
Misc 39 - Chapter 7 Class 12 Integrals - Part 3 Misc 39 - Chapter 7 Class 12 Integrals - Part 4

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Misc 39 Prove that 0 1 sin 1 = 2 1 Solving L.H.S 0 1 1 Let I = 1 Let x = sin dx = cos d Substituting in I I = 1 ( sin ) cos = cos = cos cos = (sin ) 1 sin = sin sin = sin ( cos ) = sin + cos Putting value of Hence I = sin + cos I = 1 + 1 2 = 1 + 1 2 Thus, 1 = = 1 + 1 2 Now, 0 1 1 = 1 (0) = (1) 1 1 + 1 1 0 1 0 + 1 0 = 2 (1) = = R.H.S Hence, Proved.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.