Question

"let f(x) = 4-x^2. compute the Riemann sum of f over the Interval [-1, 2] using 4 Subintervals of equal length. choose the representative points to be the left endpoints of the subintervals."

Answer 1

The question would be easier if they had asked for 3 subintervals. But if you are using 4 subintervals between -1 and 2, then the width of each one is going to be 3/4. You will be adding 4 rectangles. The width of each rectangle is 3/4 or .75. The height of the left subintervals are f(-1), f(-.25), f(.5) and f(1.25). f(-1) = 4 - (-1)^2. So f(-1) = 3. Calculate the others then add the areas of the four rectangles.