Mon Prof Augmenté
Area under a curve
Age 18 · Maths
For a positive function, the integral between two bounds is the area caught between its graph and the horizontal axis. Picture it as a shaded region whose top edge is the curve and whose sides are two vertical lines.
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In the picture
- The curve: the graph of the positive function whose height shapes the region.
- The shaded region: the area under the curve between the two bounds.
- The left vertical line: the lower bound of the interval.
- The right vertical line: the upper bound of the interval.
Examples
- Distance travelled from a speed-time graph when speed changes.
- Water collected from a rainfall rate that changes during the day.
Key takeaways
- If the curve stays above the horizontal axis, the integral gives a positive area.
- Changing either bound changes the width and size of the shaded area.
Quiz: Area under a curve (Age 18)
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For a positive function, what does the integral between two bounds represent?
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If the curve stays above the horizontal axis, what sign does the integral have?
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What happens to the shaded area if either bound is changed?
The answers, each with its explanation, are in the app. This lesson has left the free week, so its quiz is part of the subscription.
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