Final answer:
To approximate the area between the x-axis and g(x) from x=-1 to x=5 using a trapezoidal sum with 3 equal subdivisions, calculate the area of each subdivision using the trapezoid formula and then sum them up.
Step-by-step explanation:
To approximate the area between the x-axis and g(x) using a trapezoidal sum, we can divide the interval from x=-1 to x=5 into three equal subdivisions: [-1, 1], [1, 3], and [3, 5].
Using the formula for the area of a trapezoid, we can calculate the area of each subdivision and then sum them up to get the approximate total area.
For the first subdivision, the left base is 1 and the right base is 6. The height is 2 (from x=-1 to x=1). So the area is (1+6) * 2 / 2 = 7.
Similarly, for the second subdivision, the left base is 6 and the right base is 4. The height is 2 (from x=1 to x=3). So the area is (6+4) * 2 / 2 = 10.
For the third subdivision, the left base is 4 and the right base is 9. The height is 2 (from x=3 to x=5). So the area is (4+9) * 2 / 2 = 13.5.
Adding up the areas of the three subdivisions, we get the approximate total area between the x-axis and g(x) from x=-1 to x=5 as 7 + 10 + 13.5 = 30.5 square units.