At a Glance - Midpoint Sums with Shortcuts
Midpoint sum notation isn't as concise as left-hand sums and right-hand sum notation. However, we can still use similar shortcuts to find the values of f at all the points we need, add these values up, and then multiply by the width of a sub-interval. Check out the examples!
Let f(x) = 3x. Use a midpoint sum with 4 sub-intervals to estimate the area between f and the x-axis on [0, 2].