Ex 7.10, 2 - Evaluate using substitution: root sin cos 5 - Definate Integration - By Formulae

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

Transcript

Ex7.10, 2 Evaluate the integrals using substitution 0 2 sin cos 5 Let = 0 2 cos 5 = 0 2 cos 4 = sin 1 sin 2 2 Put = sin Differentiating w.r.t. = sin = cos cos = Hence, when varies form 0 to 2 , then varies form 0 to 1 Hence we can write the integrate as = 0 2 1 sin 2 2 = 0 1 1 2 2 = 0 1 1 2 2 = 0 1 1 2 2 = 0 1 1 2 1 2 2 + 4 = 0 1 1 2 2 2 + 1 2 + 4 + 1 2 = 0 1 1 2 2 3 2 + 9 2 = 1 2 +1 1 2 +1 0 1 2 3 2 +1 3 2 +1 0 1 + 9 2 +1 9 2 +1 0 1 = 3 2 3 2 0 1 2 7 2 7 2 0 1 + 11 2 11 2 0 1 = 2 3 1 3 2 0 3 2 2 2 7 1 7 2 0 7 2 + 2 11 1 11 2 0 11 2 = 2 3 4 7 + 2 11 = 154 132 + 42 231 =

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