Final answer:
To find the enclosed area between y = f(x) and y = g(x), we must determine the intersection points and then integrate the difference between f(x) and g(x) over the relevant x-coordinates. The lower integration limit c is the x-coordinate at the first intersection.
Step-by-step explanation:
To find the area of the region enclosed by y = f(x) and y = g(x) over the interval [a, b], we first need to determine where the functions intersect. This occurs at the y-coordinates where f(x) equals g(x). Given that f(x) = 1, 2, 3, 4, 5 and g(x) = 1, 2, -1, -2, we see that they intersect at the points where f(x) = 1 and f(x) = 2. The next step is to find the lower limit c for the integration. Since horizontal strips are used, we integrate with respect to x (dx).
By analyzing the given f(x) and g(x) values, we observe that they intersect at the first two points only. Therefore, the area can be calculated by integrating the difference between the functions f(x) and g(x) with respect to x. The lower limit c corresponds to the x-coordinate of the first point of intersection. Since specific x-values are not provided, we cannot explicitly find c, but the concept is to integrate from c to the x-coordinate of the second intersection point.
The infinitesimal strip method mentioned refers to summing the areas of very thin rectangles (strips) under the curve between these points. The width of each strip is an infinitesimal change in x (dx), and the height is given by the difference in the function values (f(x) - g(x)) at each x coordinate.