If ∫ cos x cos 2x cos 5x dx = A 1 sin 2x + A 2 sin 4x + A 3 sin 6x + A 4 sin 8x + c, then the values of A 1 , A 2 , A 3 , A 4 are

If ∫ cos x cos 2x cos 5x dx =... - Solved

Mathematics Definite Integrals Hard

If ∫ cos x cos 2x cos 5x dx = A1 sin 2x + A2 sin 4x + A3 sin 6x + A4 sin 8x + c, then the values of A1, A2, A3, A4 are

(A) \(A_1 = \frac 1 2,\;A_2 = \frac 1 4,\; A_3 = \frac 1 6,\; A_4 = \frac 1 8\)

(B) \(A_1 = \frac 1 8,\;A_2 = \frac 1 {16},\; A_3 = \frac 1 {24},\; A_4 = \frac 1 {32}\)

(C) \(A_1 = \frac 1 6,\;A_2 = \frac 1 {12},\; A_3 = \frac 1 {18},\; A_4 = \frac 1 {24}\)

(D) \(A_1 = \frac 1 4,\;A_2 = \frac 1 8,\; A_3 = \frac 1 {12},\; A_4 = \frac 1 {16}\)

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Correct Solution: Option B

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