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18 October, 08:48

Consider the area shown below. The top curve (in blue) is y=cuberoot (x) and the bottom curve (in red) is y=x^3, and we have used the notation Dy for delta y.

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  1. 18 October, 09:10
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    The top curve is

    y = √x

    The bottom curve is

    y = x³

    We are to find the area between the two curves, the limits are 0 and 1

    A = ∫ (x³ - √x) dy from 0 to 1

    A = x⁴/4 - (1/2) / √x |from 0 to 1

    A = 0.25 square units
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