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AP EAMCET201825 Apr 2018Morning ShiftMathematicsDefinite IntegrationActual

∫ 0 π x tan x sec x + tan x d x =

Options

  1. Aπ - 2 2
  2. Bπ + 2 2
  3. Cπ ( π + 2 ) 2
  4. Dπ ( π - 2 ) 2

Correct answer

D. π ( π - 2 ) 2

Step-by-step solution

Let I = ∫ 0 π x tan x sec x + tan x d x = ∫ 0 π π - x tan π - x sec π - x + tan π - x d x = ∫ 0 π π - x - tan x - sec x - tan x d x = ∫ 0 π π - x tan x sec x + tan x d x = ∫ 0 π π tan x sec x + tan x d x - ∫ 0 π x tan x sec x + tan x d x = ∫ 0 π π tan x sec x + tan x d x - I ⇒ 2 I = π ∫ 0 π tan x sec x + tan x d x ⇒ 2 I = π ∫ 0 π sin x cos x 1 cos x + sin x

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