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