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Curve y = a sqrt(x) + bx through (1, 2) with area 8 up to x = 4: find a and b

The same question, asked 2 times: 13 May 2024 S2, 22 Apr 2025 S2. Every wording below, oldest first.

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  1. Question 1

    13 May 2024 S2

    139
    If a curve y=ax+bxy=a\sqrt{x}+bx passes through the point (1,2)(1,2) and the area bounded by the curve, line x=4x=4 and X-axis is 8 sq. units, then

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  2. Question 2

    22 Apr 2025 S2

    120
    If a curve y=ax+bxy = a\sqrt{x}+ bx passes through the point (1,2)(1,2) and the area bounded by this curve, line x=4x = 4 and the X -axis is 8 sq. units, then the value of a−ba - b is

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