how does one know what "the central third" of a 10 m box is? I need to take an integral and I need to know the limits. Central third I'd say is 1/3 to 2/3? but I really don't know.

Yes, I think that is the intent of the fuzzy phrasing :)

thank you! I prefer direct instructions haha.

To determine the central third of a 10 m box, you first need to understand what is meant by "central third." In this context, the central third refers to the interval within the box that spans one-third of its total length, positioned in the middle.

To find the limits for the central third of the box, you can follow these steps:

1. Determine the total length of the box. In this case, it is given as 10 m.

2. Calculate one-third of the total length by dividing it by 3. So, (10 m) / 3 = 3.33 m (approximately).

3. Subtract this value from the total length to find the upper limit of the central third. In this case, 10 m - 3.33 m = 6.67 m (approximately).

4. Similarly, add the one-third value to the total length to find the lower limit of the central third. So, 10 m + 3.33 m = 13.33 m (approximately).

Therefore, the limits for the central third of the 10 m box are approximately 3.33 m and 6.67 m. These limits will help you set up the appropriate integrals for your calculations.