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Solution: This has got to be an odd looking curve. Start by looking at where the curve crosses the axes. At x = 0, y = -2 and at y = 0, x = 4. One other point, x = 1, y = -1, is sufficient, along with the points where the curve crosses the axes, to sketch the curve. |
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The shaded area is the only area between the curve and the axes. The area is
The area ist negative! Are areas below the axis negative? Just to be sure, change the limits on the integral to 4 and 5 and see if that area comes out positive, as we would expect from the graph.
This area comes out positive and very small, about as expected considering the curve.
Problem AUC07 illustrates an important point. Be careful when finding an area below the axis. You can end up with a negative number for the area. The following problem, AUC20, is a typical test problem involving positive and negative area. There is a simple way to handle this negative area situation as illustrated in this problem.
