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AP EAMCET202119 Aug 2021Morning ShiftMathematicsIndefinite IntegrationActual

If ∫ 1 - ( cot x ) 2021 tan x + ( cot x ) 2022 d x = 1 A log ( sin x ) 2023 + ( cos x ) 2023 + c , then A = ______

Options

  1. A2020
  2. B2021
  3. C2022
  4. D2023

Correct answer

D. 2023

Step-by-step solution

Given that ∫ 1 - c o t x 2021 tan x   + c o t x 2022   d x = ∫ sin x 2021   -   cos x 2021 sin x 2021 × sin x 2022 cos x sin x 2023 + cos x 2023 d x = ∫ sin x 2021   -   cos x 2021 1 × sin x cos x sin x 2023 + cos x 2023 d x = ∫ sin x 2022 cos x - cos x 2022 sin x sin x 2023 + cos x 2023 d x =   1 2023 ∫ f ' x f x d x   =   1 2023 ln f x +   c So A   =   2023 .

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