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Integral of a modulus |f(x)|: split where f(x) changes sign

This type of question, asked 9 times: 10 May 2023 S1, 12 May 2024 S1, 12 May 2024 S2, 20 Apr 2025 S1, 26 Apr 2025 S2, 15 Apr 2026 S2, 18 Apr 2026 S2, 19 Apr 2026 S2, 20 Apr 2026 S2. All 9 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    10 May 2023 S1

    101
    ∫0π/2∣sin⁡x−cos⁡x∣ dx\int_0^{\pi/2}|\sin x - \cos x|\,dx has the value

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  2. Question 2

    12 May 2024 S1

    145
    ∫04∣2x−5∣ dx=\displaystyle\int_{0}^{4}|2x-5|\,dx=

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  3. Question 3

    12 May 2024 S2

    106
    The value of ∫0π∣sin⁡x−2xπ∣ dx\int_0^{\pi} \left|\sin x - \frac{2x}{\pi}\right|\,dx is

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  4. Question 4

    20 Apr 2025 S1

    123
    ∫−22∣x2−x−2∣dx=\int_{- 2}^{2} \left| x^{2}-x- 2 \right|dx=

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  5. Question 5

    26 Apr 2025 S2

    105
    ∫01x∣x−12∣dx=\int_{0}^{1} x\left| x-\frac{1}{2} \right|dx=

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  6. Question 6

    15 Apr 2026 S2

    81
    ∫0π∣sin⁡2x∣ dx=\displaystyle\int_0^\pi|\sin 2x|\,dx =

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  7. Question 7

    18 Apr 2026 S2

    81
    ∫02∣4x−5∣ dx=…\int_0^2|4x - 5|\,dx = \ldots

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  8. Question 8

    19 Apr 2026 S2

    79
    If f(x)=∣5x−3∣f(x) = |5x - 3| is defined on interval [0,1][0, 1], then the value of ∫01f(x) dx\int_0^1 f(x)\,dx is...

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  9. Question 9

    20 Apr 2026 S2

    82
    The value of the integral ∫1/ee∣log⁡x∣x2 dx\int_{1/e}^{e}\dfrac{|\log x|}{x^2}\,dx is

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