# What is the net area between f(x) = 3x^2-x+2 and the x-axis over x in [1, 3 ]?

Sep 17, 2016

Net area $= 26$

#### Explanation:

Given -

$f \left(x\right) = 3 {x}^{2} - x + 2$

Area under the curve between $x = 1$ and $x = 3$

${\int}_{1}^{3} \left(3 {x}^{2} - x + 2\right) = {\left[{x}^{3} - {x}^{2} / 2 + 2 x\right]}_{1}^{3}$

$\left[{3}^{3} - {3}^{2} / 2 + 2.3\right] - \left[{1}^{3} - {1}^{2} / 2 + 2.1\right]$

$\left[27 - \frac{9}{2} + 6\right] - \left[1 - \frac{1}{2} + 2\right]$

$\frac{57}{2} - \frac{5}{2} = 52 - 2 = 26$

Net area $= 26$