Question

Find the area of the region enclosed by f(x) and the x-axis for the given function over the specified interval x2 + 2x +2 x

Answer 1

In order to determine the area in the interval [-3, -3] of the function enclosed by:

$f(x)=\begin{cases}x^2+2x+2 \\ 3x-4\end{cases}$

When the first term is for x<2 and the second when x>=2.

We proceed as follows:

$\int ^3_{-3}(x^2+2x+2)-(3x-4)\rbrack dx$$\Rightarrow\int ^3_{-3}(x^2-x+6)dx=\frac{x^3}{3}-\frac{x^2}{2}+6x|^3_{-3}=54$