### Home > APCALC > Chapter 6 > Lesson 6.1.2 > Problem6-27

6-27.

Earlier, Jamal wrote the Riemann Sum $\displaystyle\sum _ { i = 0 } ^ { 9 } \frac { 1 } { 2 } f ( - 3 + \frac { 1 } { 2 } i )$, to estimate the area under $f(x) = 3x^2 - 2$ over the interval $[–3, 2]$ using $10$ rectangles.

1. Use the summation feature of your calculator to approximate the area using Jamal’s Riemann sum.

$29.375\ \text{un}²$

2. Calculate the exact area using an integral.

First set up an integral on the given interval.

$\int_{-3}^{2}(3x^{2}-2)dx$