Find the approximate area between the curve f(x) = -4x² + 32x and on the x-axis on the interval [0,8] using 4 rectangles. Use the right endpoint of each rectangle to determine the height.

Split up the interval [0, 8] into 4 equally spaced subintervals:

[0, 2], [2, 4], [4, 6], [6, 8]

Take the right endpoints, which form the arithmetic sequence

where 1 ≤ i ≤ 4.

Find the values of the function at these endpoints:

The area is given approximately by the Riemann sum,

where ; so the area is approximately

where we use the formulas,