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This is easier to understand when the graph is horizontal.

Speed is defined as distance / time. Rearranging the equation: distance = speed x time. In the graph, that would be proportional to the area of the rectangle under the (horizontal) speed line.

If speed is variable, the graph can be approximated by many small rectangles. The same reasoning as above applies to each one. This method - of separating an area into many small parts - is called "integration".

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Q: Why the area under a speed-time graph gives distancestan?
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