Final answer:
The provided question is about calculating weight using a scale, but it lacks sufficient information and context to establish a reliable integral for determining weight. Without more details, an integral representing the weight cannot be accurately formed.
Step-by-step explanation:
The question seems to be asking about calculating weight using the given scale factor and requires setting up an integral to find the weight W. This involves understanding both the physics concept of weight as a force and the mathematical concept of integration. However, the question appears to be incomplete, and lacks a clear context and sufficient data to form an accurate integral expression. Therefore, a proper solution cannot be provided without more specific information. Typically, the weight W is found by multiplying mass by the acceleration due to gravity (W = mg), but this doesn't seem to align with the information provided in the question.