Create a grid to provide upper and lower bounds on the area under the curve y=4x-x^2 using 8 rectangles of equal width for each bound

Expert Answers
rcmath eNotes educator| Certified Educator

Let's start by finding the x-intercepts.

`4x-x^2=0=>x(4-x)=0=>x=0 or x=4` 

If we graph the function we will notice that the area under the curve and above the x-axis is between the two intercept. Hence our interval is [0,4]. We need to divide that into 8 equal parts, thus `Deltax=4/8=0.5`

Let's find the area by using f(0) for the height of the first rectangle, etc.






Given the symetric nature of the curve over the interval [0,4], we ended up with the lower and upper bound equal.