Question

Asked Feb 23, 2019

Given the function f(x)=−x−2, find the total area between f(x) and the x-axis over the interval [−5,−1].

Step 1

To find the area of the given region which may lie both above and below the x-axis.

Step 2

The graph of y=-2-x is drawn by joining the points (-5,3) and (-1,-1). Notice that the graph lies both above (between x=-5 and x=-2) and below (between x=-2 and x=-1) the x-axis. The total area of the region required is computed ignoring the sign of the area (note that the area below the x-axis will have negative sign, if the sign is taken into account)

Step 3

The area under a curve is normally computed as a definite integral. In our case , the two regions are right angl...

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