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JEE Main202229 Jul 2022Evening ShiftMathematicsIndefinite IntegrationActual

For I x = ∫ sec 2 x - 2022 sin 2022 x d x , if I π 4 = 2 1011 , then

Options

  1. A3 1010 I π 3 - I π 6 = 0
  2. B3 1010 I π 6 - I π 3 = 0
  3. C3 1011 I π 3 - I π 6 = 0
  4. D3 1011 I π 6 - I π 3 = 0

Correct answer

A. 3 1010 I π 3 - I π 6 = 0

Step-by-step solution

Given, I x = ∫ sec 2 x - 2022 sin 2022 x d x On rearranging we get, ⇒ I x = ∫ sec 2 x ⏟ I I · sin - 2022 x ⏟ I d x - 2022 ∫ sin - 2022 x d x Now using integration by parts we get, ⇒ I x = tan x . sin x - 2022 + ∫ 2022 tan x · sin x - 2023 cos x d x - 2022 ∫ sin x - 2022 d x ⇒ I x = tan x . sin x - 2022 + ∫ 2022 tan x · sin x - 2022 cos x sin x d x - 2022 ∫ sin x - 2022 d x ⇒ I x = tan x . sin x - 2022 + ∫ 2022 sin x -

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