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2-85.

Jamal wrote the following Riemann sum to estimate the area under $f(x) = 3x^2-2$
$\displaystyle\sum _ { i = 0 } ^ { 9 } \frac { 1 } { 2 } f ( - 3 + \frac { 1 } { 2 } i )$

1. Draw a sketch of the region. How many rectangles did he use?

General form of left-endpoint Riemann Sum:
$\displaystyle\sum_{i=0}^{n-1}\Delta xf(a+\Delta xi)$

$n − 1 = 9 n = 10$ There are $10$ rectangles.

The function is $f(x) = 3x^² − 2$

$a = −3$ This is where the region starts.

$\Delta x=\frac{1}{2}$
Each rectangle has a width of $\frac{1}{2}$.

2. For what domain of $f(x)$ did Jamal estimate the area?

Refer to the graph in part (a).

3. Use the summation feature of your calculator to find the approximate area using Jamal's Riemann sum.

Use the eTool below to complete the problem.
Click on the link to the right to view the full version of the eTool. Calc 2-85 HW eTool