The area under a graph of force against distance (or extension, if it's a spring) represents the work done by that force. Since it sounds like you're talking about a spring, you should know that the area would represent the work done to stretch the spring that distance, and also represents the amount of elastic potential energy contained by the spring.
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Nothing in particular. It certainly does not represent acceleration.
It can represent the graph of a strict inequality where the inequality is satisfied by the area on one side of the dashed line and not on the other. Points on the line do not satisfy the inequality.
An area graph. It fills the area between a line and the line below or the x-axis.
line graph!
Of course not! The solution to some equations could represent the area under a curve, or the volume of some shape, or the rate of change in something.