Chapter 4.3, Problem 17C

a.

To determine

To write:An n-rectangle right sum for ${\displaystyle \underset{0}{\overset{3}{\int }}{x}^{2}dx}$ and a sum formula in terms of n.

b.

To determine

To write: An n-rectangle left sum for ${\displaystyle \underset{0}{\overset{3}{\int }}{x}^{2}dx}$ and a sum formula in terms of n.

c.

To determine

To prove: The right sum and the left sum for ${\displaystyle \underset{0}{\overset{3}{\int }}{x}^{2}dx}$ are different for $n=100$ and $n=1000$ .

d.

To determine

To prove: The right sum and the left sum for ${\displaystyle \underset{0}{\overset{3}{\int }}{x}^{2}dx}$ approach the same quantity as $n\to \infty$ .