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JEE Main202324 Jan 2023Morning ShiftMathematicsDefinite IntegrationActual

The value of 8 π ∫ 0 π 2 cos x 2023 sin x 2023 + cos x 2023 d x is ______.

Correct answer

0

Step-by-step solution

Let I = 8 π ∫ 0 π 2 cos x 2023 sin x 2023 + cos x 2023 d x       . . . 1 Using ∫ 0 a f ( x ) dx = ∫ 0 a f ( a - x ) dx I = 8 π ∫ 0 π 2 sin x 2023 sin x 2023 + cos x 2023 d x       . . . 2 Adding 1 and 2 , we get 2 I = 8 π ∫ 0 π 2 1   dx ⇒ 2 I = 8 π x 0 π 2 ⇒ I = 2

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