use the limit process to find the area of the region between f(x) = x^2 + 2 and the x axis on the interval [0,3]

use the limit process to find the area of the region between f(x) = x^2 + 2 and the x axis on the interval [0,3]

$f(x)=x^{2} + 2$

$\int_{0}^{3} \! f(x) \, dx= \int_{0}^{3} \! \left(x^{2}+2\right) \, dx$ =  $​\left[\frac{x^{3} }{3}+2x \right]_{0}^{3}$

$=\left[9+ 6\right]-\left[0\right] = 15$