Area beneath a curve

A curve and a horizontal axis bound a shaded region. Adding up thin rectangular strips approximates that region, and making the strips narrower gives the integral.

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Age 17: open this week

In the picture

1: the curved boundary line above
2: the shaded region between the curve and the axis
3: one thin vertical strip used to approximate area
4: the horizontal axis segment under the shaded region

Examples

Distance travelled over time from a speed curve
Total water flow from a varying flow-rate curve

Key takeaways

The integral accumulates infinitely thin slices of area.
The area under a curve can represent a total quantity.

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