Chapter 14.5, Problem 11AYU

The function $f(x)=-3x+9$ is defined on the interval $\left[0,3\right].$

1. Graph $f.$

   In $(b)-(e),$ approximate the area $A$ under $f$ from $0$ to $3$ as follows:

2. Partition $\left[0,3\right]$ into three subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

3. Partition $\left[0,3\right]$ into three subintervals of equal length and choose $u$ as the right endpoint of each subinterval.

4. Partition $\left[0,3\right]$ into six subintervals of equal length and choose $u$ as the left endpoint of each subinterval.

5. Partition $\left[0,3\right]$ into six subintervals of equal length and choose $u$ as the right endpoint of each subinterval.

6. What is the actual area $A$?