Calculus/Cal 2·area-between-curves

Area Between Curves

Determine the area enclosed between two specified curves over a defined interval.

Math animationCalculus/Cal 2 · area-between-curves

✓ All 2 test cases pass.

Inputs

Upper Curve

The equation of the upper curve.

Lower Curve

The equation of the lower curve.

Start of Interval

The starting point of the interval.

End of Interval

The ending point of the interval.

Test cases

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#	Inputs	Expected	Got	Status
1	{"upper_curve":"5*x - x^2","lower_curve":"x","interval_start":0,"interval_end":5}	8.33333	8.333333333333332	✓
2	{"upper_curve":"x^2","lower_curve":"0","interval_start":0,"interval_end":2}	2.66667	2.666666666666665	✓

APIDeveloper APICall this calculator from codeexpand ↓

Endpoint

POST/api/calculators/calculus-cal-2/area-between-curves/compute

Inputs (4)

upper_curveexpressiondefault "5*x - x^2"
lower_curveexpressiondefault "x"
interval_startnumberdefault 0
interval_endnumberdefault 5

Example

curl -sX POST http://localhost:3001/api/calculators/calculus-cal-2/area-between-curves/compute \
  -H "Content-Type: application/json" \
  -d '{"inputs":{"upper_curve":"5*x - x^2","lower_curve":"x","interval_start":0,"interval_end":5}}'

Try it live

Edit the body below, then click Call API.

Request body

Response

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full API docs →

Source: Pattern from: Calculus II Final Exam Review.pdf. Reproduces a standard area-between-curves computation; problem text paraphrased.

AI disclosure: Calculator code generated by openai/gpt-4o-mini-2024-07-18; verified by 2 test cases.