Final answer:
To approximate the area under the graph of f(x), divide the interval (1, 5) into 4 subintervals and use the left endpoint of each subinterval. The area of each rectangle is -2 * 1 = -2, and since there are 4 rectangles, the total area is the absolute value of -8, which is 8.
Step-by-step explanation:
To approximate the area under the graph of f(x), we can divide the interval (1, 5) into 4 subintervals and use the left endpoint of each subinterval. In this case, f(x) = -2 for all values of x, so the height of each rectangle will be -2. The width of each subinterval can be calculated by dividing the total width of the interval, which is 5 - 1 = 4, by the number of subintervals, which is 4. Each subinterval will have a width of 4/4 = 1. Therefore, the area of each rectangle will be -2 * 1 = -2.
The total area can be calculated by summing up the areas of all the rectangles. Since there are 4 rectangles, the total area will be -2 + (-2) + (-2) + (-2) = -8. However, since area cannot be negative, we take the absolute value of the result to get the final answer, which is 8.
Therefore, the approximate area under the graph of f(x) over the interval (1, 5) using 4 subintervals and the left endpoint of each subinterval is 8.