It's Another Trigonometric Integral!

Calculus Level 2

A = ∫ 0 π sin ⁡ 2 x cos ⁡ x − 2 sin ⁡ x 12 cos ⁡ 4 x cos ⁡ 2 x sin ⁡ x + 8 sin ⁡ 4 x sin ⁡ 2 x sin ⁡ x − 7 cos ⁡ 4 x sin ⁡ x − 2 sin ⁡ x cos ⁡ 6 x − 14 sin ⁡ 3 x sin ⁡ 2 x − 3 sin ⁡ 2 x cos ⁡ x + sin ⁡ x d x A=\int_{0}^{\pi}\dfrac{\sin2x\cos x-2\sin x}{12\cos 4x\cos 2x\sin x+8\sin 4x \sin 2x \sin x-7\cos 4x\sin x -2\sin x \cos 6x -14\sin 3x\sin^2x -3\sin 2x \cos x+\sin x}dx Find π A \dfrac{\pi}{A}

Inspiration


The answer is 2.

Zakir Husain by Zakir Husain , 41, India

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