# Midpoint Sums with Shortcuts Exercises

### Example 1

Use a midpoint sum with 5 sub-intervals to estimate the area between *f*(*x*) =* x*^{2} and the *x*-axis on [0, 1].

### Example 2

Use a midpoint sum with 10 sub-intervals to estimate the area between *f*(*x*) = *x*^{2} and the *x*-axis on [0, 1].