Ex 7.2, 34 - Integrate root(tan x) / sin x cos x - Integration by substitution - Trignometric - Normal

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

Transcript

Ex 7.2, 34 tan sin cos tan sin cos The given function cannot be integrated by direct substitution, Step 1: Simplify the given function tan sin cos = tan sin cos . cos cos = tan sin . cos 2 cos = tan cos 2 . sin cos = tan cos 2 . tan = tan 1 2 1 1 cos 2 = tan 1 2 1 cos 2 = tan 1 2 sec 2 tan sin cos = tan 1 2 sec 2 Step 2: Integrating the function tan sin cos . = tan 1 2 sec 2 . Let tan = Differentiating both sides . . . sec 2 = = sec 2 Thus, our equation becomes tan 1 2 . sec 2 . = 1 2 . sec 2 . sec 2 = 1 2 . = 1 2 +1 1 2 +1 + = 1 2 1 2 + = 2 1 2 + = 2 + = +

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