Area of Revolution Calculator

Area of Revolution Calculator calculator can be used to calculate the area of a solid of revolution formed by rotating a curve around an axis.

Input Parameters

Calculation Results

Calculation Formula

The area of the solid of revolution formed by rotating the curve y = f(x) around the x-axis from a to b is given by:

A = π ∫ab [f(x)]² dx

Where:
- f(x) is the function
- π is the mathematical constant Pi (~3.14159)
- a and b are the lower and upper limits of integration

Area of Revolution Calculator Calculator Usage Guide

Learn how to use the Area of Revolution Calculator calculator and its working principles

How to Use the Calculator

  1. Enter the function f(x) in the input field. For example, you can enter x^2, sin(x), or 1/x.
  2. Select the rotation axis (x-axis or y-axis).
  3. Enter the lower limit (a) and upper limit (b) for the integral.
  4. Click the "Calculate" button to compute the area of the solid of revolution.
  5. The result will be displayed in the result field.

Example

Let's calculate the area of the solid formed by rotating the function y = x^2 around the x-axis from x = 0 to x = 1.

  1. Enter x^2 in the function field.
  2. Select the x-axis as the rotation axis.
  3. Set the lower limit to 0 and the upper limit to 1.
  4. Click "Calculate".
  5. The result will be π/3 ≈ 1.0472.

Notes

  • The calculator uses numerical integration to approximate the area. For more accurate results, ensure the function is properly defined and the limits are within a valid range.
  • For rotation around the y-axis, the function should be expressed in terms of y. For example, if rotating y = x around the y-axis, you should enter x as the function.