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
- A2020
- B2021
- C2022
- 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 .