Problem One:

In this problem, we are asked to find the area of a rectangle that measures 6 feet by 40 feet. The area of a rectangle is the product of its two dimensions. Thus, the area we require is the product of 6 feet and 40 feet, which equals 240 square feet. Expressed as an integral, and calling the distance along the shorter dimension, "x," the area is, "The integral from x-equals-zero-feet to x-equals-six-feet of 40-feet-dee-x," which again equals 240 square feet.