The slope of a velocity-time graph is known to give the acceleration while the area under the graph speaks of the displacement of a body. This is some of the earliest physics students learn. Essentially, this is a simplification of the process of integration. The slope is the differentiation,
and the area is the classic picture of how integration works as a computation of the areas of a series of rectangles:
Moving to a position-time, or displacement-time, graph now, we find that the differentiation bit still holds: the slope gives us the velocity, which is unsurprising. However, I always thought that the area under the displacement time graph was physically meaningless even if mathematically interesting (although I cannot vouch for its mathematical image).
A portmanteau between absent and position, or between absent and displacement, the integral given by
Old NID
177927
