For the following three (03) items: Consider the function f(x) =...

The given function is $f(x) = x|x|$.

The required area bounded by the curve $f(x)$, the $x$-axis and the lines $x = -2$ and $x = 1$ is given by:

$A = \int_{-2}^{1} |f(x)| dx$

$A = \int_{-2}^{1} |x|x|| dx$

Since $|x|x|| = |x|^2 = x^2$, we have:

$A = \int_{-2}^{1} x^2 dx$

$A =$\left[ \dfrac{x^3}{3} \right]_{-2}^{1}$<br><br>$A = \dfrac{1^3}{3} - \dfrac{(-2)^3}{3}$<br><br>$A = \dfrac{1}{3} - \left( -\dfrac{8}{3} \right)

$A =$\dfrac{9}{3} =3$<br><br>Answer:$3