Final answer:
To replace distributed loading with an equivalent resultant force, integration is the correct method used in engineering. It allows for the calculation of total force over a length or area, simplifying continuous distributions of forces into a single force for easier analysis.
Step-by-step explanation:
To replace the distributed loading with an equivalent resultant force, the correct method to use is Integration (Option A). This is because integration allows you to calculate the total force represented by a distributed load over a certain length or area. In engineering, specifically in statics and dynamics, this process is often used in beam calculations where a continuous distribution of forces is simplified into a single resultant force.
When applying the science practices related to sums of forces, it's crucial to understand that forces are vector quantities. Thus, the net force acting on a system will be the vector sum of all the forces involved. In some cases, internal forces may cancel out, resulting in an overall force that can be simpler to reckon with when considering the force’s direction and magnitude, an essential part of statics and dynamics problems.
The concept of integration extends to various parameters in engineering, such as velocity and energy. When a formula requires an average or most probable value, as is common in calculating distribution functions, the integration of a continuous variable is necessary. For example, an average velocity implies integrating a velocity distribution function over possible speeds.