find the riemann sum

Question

Find the Riemann sum for  over the domain interval , partitioned into rectangles divided at  with rectangle heights  evaluated at . Express the answer to at least three decimal places.

Answer 1

First, locate the dividing points, namely,0, 0.5, 1.5, 3, 5, 8

Next, find the length of each subdivision, 0.5, 1, 1.5, 2, 3

Then, locate the points of evaluation, 0.25, 1, 2, 4, 8

The Riemann Sum is given by the sum of the (length of interval)*(value of the functions at the point of evaluation).

The answer is (sqrt(0.25))*0.5 + (sqrt(1))*1 + (sqrt(2))*1.5 +(sqrt(4))*2 + (sqrt(8))*3 = 15.856