Calculus/Cal 2·volume-of-revolution

Volume Of Revolution

Calculate the volume of a solid formed by rotating a specified region around the x-axis, defined by two curves.

Math animationCalculus/Cal 2 · volume-of-revolution

✓ All 2 test cases pass.

Inputs

First curve equation

The equation of the first curve in terms of y.

Second curve equation

The equation of the second curve in terms of y.

Axis of rotation

The axis around which the region is rotated.

Test cases

These cases run live in your browser every time the page loads. If any fail, the calculator is broken — file an issue.

#	Inputs	Expected	Got	Status
1	{"curve1":"2*x","curve2":"x^2","axis":"x-axis"}	13.404129	13.404128655315613	✓
2	{"curve1":"x","curve2":"x^2","axis":"x-axis"}	0.418879	0.41887902047861303	✓

APIDeveloper APICall this calculator from codeexpand ↓

Endpoint

POST/api/calculators/calculus-cal-2/volume-of-revolution/compute

Inputs (3)

curve1expressiondefault "2*x"
curve2expressiondefault "x^2"
axisstringdefault "x-axis"

Example

curl -sX POST http://localhost:3001/api/calculators/calculus-cal-2/volume-of-revolution/compute \
  -H "Content-Type: application/json" \
  -d '{"inputs":{"curve1":"2*x","curve2":"x^2","axis":"x-axis"}}'

Try it live

Edit the body below, then click Call API.

Request body

Response

(click Call API to see the response)

full API docs →

Source: Pattern from: Calculus II Final Exam Review.pdf. Reproduces a standard volume-of-revolution computation; problem text paraphrased.

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