Answer:
To find the volume of the pyramid using integration, we can consider dividing the pyramid into an infinite number of small horizontal slices. Each slice will be a rectangle with width "dx" and length equal to the corresponding side of the square base. Let's denote the variable "x" as the height of each slice, starting from the base of the pyramid. The width of each slice, "dx," will represent a small change in height as we move from the base to the top. The area of each slice can be calculated as the area of a square base, which is "s^2," multiplied by the width "dx." So, the area of each slice is "s^2 * dx." To find the volume of the entire pyramid, we need to sum up the volume of all these small slices. This can be done by integrating the area function from x=0 (base of the pyramid) to x=h (top of the pyramid): Volume = ∫[0 to h] s^2 * dx In this case, s=1340 and h=1280. Integrating the function gives us: Volume = ∫[0 to 1280] 1340^2 * dx Volume = 1340^2 * ∫[0 to 1280] dx Integrating the function "dx" with respect to "x" simply gives us "x": Volume = 1340^2 * [x] [0 to 1280] Now, we can substitute the values of x=1280 and x=0 into the expression: Volume = 1340^2 * [1280 - 0] Volume = 1340^2 * 1280 Volume = 227,072,000 cubic units So, the volume of the pyramid is 227,072,000 cubic units. Note: It's important to understand that this is just one way to approach the problem. There may be alternative methods to find the volume of the pyramid using integration, but this is a commonly used approach.