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Area bounded by the parabola y = x^2 + c, a straight line, the Y-axis and a vertical line

The same question, asked 4 times: 3 May 2023 S2*, 4 May 2023 S2*, 9 May 2023 S2*, 19 May 2026 S2. Every wording below, oldest first.

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  1. Question 1

    3 May 2023 S2

    111
    The area of the region, bounded by the parabola y=x2+2y=x^{2}+2 and the lines y=x, x=0y=x,\,x=0 and x=3x=3, is

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  2. Question 2

    4 May 2023 S2

    114
    The area (in square units) in the first quadrant bounded by the curve y=x2+2y=x^2+2 and the lines y=x+1,x=0y=x+1, x=0 and x=3x=3, is

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  3. Question 3

    9 May 2023 S2

    110
    The area (in sq. units), in the first quadrant bounded by the curve y=x2+2y = x^2 + 2 and the lines y=x+1,x=0y = x+1, x = 0 and x=2x = 2, is

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  4. Question 4

    19 May 2026 S2

    84
    The area bounded by the curve y=x2+4,x=y,x=3,y = x^2 + 4, x = y, x = 3, and Y-axis is

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