# Do find the area of the region?


\begin{align}&f(x)=x^3-x^2-6x\end{align}\$'como find the area of the region between the curve of the previous function? and the X axis. The area is expressed in units of surface.

Suggestion: Make the graph for a better understanding of the exercise.`

It is a parable cubic with positive coefficient for x^3, so that starts to the left -infinite and ends to the right at +infinity. Factorizándola, has three real roots, that is to say: three crossings with the x axis: (-2); 0; 3. Has two regions comprised between the curve and the x-axis: to the left above the axis (positive), and right below it (area denial). To find the total area "enclosed" between the curve and the x-axis, we must add the "modules" of these areas (that is, to take both as positive). Integrate first to get the indefinite: (1/4)x^4 - (1/3)x^3 - 3x^2 I get the two areas separately: Between (-2) and 0: 0 - $4+(8/3) - 12$: (16/3) Between 3 and 2: $(81/4) - 9 - 27$ - $4-(8/3)-12$; (-63/4) + (32/3); (-189+128)/12; (-61/12). Let us remember that we must take it as a positive: (16/3) + (61/12) = (64+61)/12; \ #### 125/12 units^2