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

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise

Transcript

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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