Question

can someome please explain this, I got that only 2 was correct but that's not a choice. please and thank you

Answer 1

The answer is B) 2 and 3

When you do a Riemann's sum, you split the interval into columns. In choice 3 we are told that there are 4 equal subdivisions meaning that each of the 4 columns are 1 wide. Since it is a left Riemann's sum we add the height of the column where the LEFT side crosses the curve. For [-1, 0], the height is -1, for [0, 1] it is 0, for [1, 2] it is 2, and for [2, 3] it is 3. Now add the heights together to get 4. Then you multiply by the width, but since the columns are 1 wide, the answer is still just 4.