Midpoint Sums with Shortcuts - At A Glance

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!

Examples
Exercises

Example 1

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].

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Exercise 1

Use a midpoint sum with 5 sub-intervals to estimate the area between f(x) = x² and the x-axis on [0, 1].

Exercise 2

Use a midpoint sum with 10 sub-intervals to estimate the area between f(x) = x² and the x-axis on [0, 1].