Mathematically, the area underneath the graph of a curve is the value you get by integrating that curve. From classical mechanics, one knows that the integral of an object's velocity with respect to time gives you that object's position as a function of time. Thus, the area underneath the velocity time graph from one point in time to another is the change in position of that object between those two times or, it's distance traveled.
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The area under the normal curve is ALWAYS 1.
In statistics you can find the area under a curve to establish what to expect between two input numbers. If there is a lot of area under the curve the graph is tall and there is a higher probability of things occurring there than when the graph is low.
put it in the fridge
The area is 0.008894
Since a parabola is an open infinite curve, the area inside it is infinite.