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Integral of |trigonometric expression| by splitting at its zeros

This type of question, asked 3 times: 2021 Paper 25, 29 Jan 2024, 21 Jan 2026 S1. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 25

    90
    The value of the integral ∫0π∣sin⁡2x∣dx\int_{0}^{\pi} |\sin2x|dx is

  2. Question 2

    29 Jan 2024

    174
    If ∫π6π31−sin⁡2xdx=α+β2+γ3\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sqrt{1 - \sin2x}dx=\alpha+\beta\sqrt{2}+\gamma\sqrt{3}, where α,β\alpha,\beta and γ\gamma are rational numbers, then 3α+4β−γ3\alpha+ 4\beta-\gamma is equal to

  3. Question 3

    21 Jan 2026 S1

    75
    6∫0π∣(sin⁡3x+sin⁡2x+sin⁡x)∣dx6\int_{0}^{\pi} |(\sin3x + \sin2x + \sin x)|dx is equal to