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JEE Main20231 Feb 2023Evening ShiftMathematicsDefinite IntegrationActual

If ∫ 0 π 5 cos x 1 + cos x cos 3 x + cos 2 x + cos 3 x cos 3 x d x 1 + 5 cos x = k π 16 , then k is equal to _____ .

Correct answer

0

Step-by-step solution

Given, I = ∫ 0 π 5 cos x 1 + cos x cos 3 x + cos 2 x + cos 3 x cos 3 x 1 + 5 cos x d x   . . . . 1 Now using the property ∫ a b f x d x = ∫ a b f a + b - x d x we get, ⇒ I = ∫ 0 π 5 - cos x 1 + cos x cos 3 x + cos 2 x + cos 3 x cos 3 x 1 + 5 - cos x d x     . . . . 2 Now adding above equations we get, 2 I = ∫ 0 π 1 + cos x cos 3 x + cos 2 x + cos 3 x cos 3 x d x Now using the property ∫ 0 2 a f x d x = 2 ∫ a a f x d x   when  f

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