Question

when working with riemman sums, if i divide a certain interval into lets say 4 subintervals, and i evaluate them at right endpoints, the function is 1-x^2 from [0,2], and i find that one of the rectangles has negative height, that is below the x-axis and the rest stay above the x-axis can i still sum up the area of the recatangles and get an axpproimation of the area under the curve?

Answer 1

sure...why not :)

Answer 2

okay, i just wanted to make sure, that i could still do that even though one of the rectangles height went to -.75

Answer 3

Unless it is a fluke, the Riemann sum is just an approximation. It could be a good approx or it can be a very poor approximation depending on the sample points used.