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Area between a curve that crosses the X-axis and the X-axis (split at the roots)

This type of question, asked 3 times: 9 May 2024 S2, 10 May 2024 S2, 18 Apr 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    9 May 2024 S2

    138
    The area (in sq. units) bounded by the curve y=x∣x∣y = x|x|, X-axis and the lines x=−1x = -1 and x=1x = 1 is

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  2. Question 2

    10 May 2024 S2

    109
    The area bounded by the X-axis and the curve y=x(x−2)(x+1)y=x(x-2)(x+1) is

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  3. Question 3

    18 Apr 2026 S2

    82
    If the area bounded by y=x3+axy = x^3 + ax (where a>0a > 0), the xx-axis and the lines x=−2x = -2 and x=1x = 1 is 374\dfrac{37}{4} square units, then …\ldots

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