Evaluate Riemann sum, find R6

Question

If f(x) = 5x² − 8x, 0 ≤ x ≤ 3,

 evaluate the Riemann sum with n = 6, taking the sample points to be right endpoints.

R₆ = 

Answer 1

The six rectangles you would use would span the following ranges: [0, 0.5], [0.5, 1], [1, 1.5], [1.5, 2], [2, 2.5], and [2.5, 3]. So the six right endpoints to use are 0.5, 1, 1.5, 2, 2.5, and 3. The width of each of these rectangles is 0.5. So the sum you would evaluate is:

0.5 * ( f(0.5) + f(1) + f(1.5) + f(2) + f(2.5) + f(3) )

Can you evaluate this on your own to get the final answer?