find the upper and lower bounds on the area under the curve y=4x-x^2

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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Supposing that you need to find the upper and lower bounds on the area under the given curve and x axis, then you need to solve the equation `4x - x^2 = 0 ` to find x intercepts that represent the upper and lower bounds such that:

`4x - x^2 = 0`

You need to factor out x such that:

`x(4-x) = 0 =gt x_1 = 0`

`4 - x = 0 =gt x_2 = 4`

Hence, evaluating the lower bound yields `x=0 ` and evaluating the upper bound yields `x=4` .

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