1. What is a Volume of Revolution Calculator?

Definition: This calculator computes the volume of a solid formed by rotating a function around the x-axis between two points.

Purpose: It helps students and professionals solve calculus problems involving volumes of revolution.

2. How Does the Calculator Work?

The calculator uses the disk method formula:

Where:

• \( V \) — Volume of the solid (cubic units)
• \( f(x) \) — Function being rotated (e.g., x^2, sin(x))
• \( a \) — Lower limit of integration
• \( b \) — Upper limit of integration

Explanation: The method sums up infinitely thin disks along the x-axis to calculate the total volume.

3. Importance of Volume Calculations

Details: These calculations are fundamental in engineering, physics, and mathematics for determining volumes of complex shapes.

4. Using the Calculator

Tips: Enter the function (use standard math notation), integration limits (b > a), and click Calculate.

5. Frequently Asked Questions (FAQ)

Q1: What functions can I enter?
A: Most standard functions: polynomials (x^2), trigonometric (sin(x)), exponential (e^x), etc.

Q2: What if I get an error?
A: Check your function syntax and ensure upper limit > lower limit.

Q3: Can I rotate around the y-axis instead?
A: This calculator uses x-axis rotation. For y-axis, you'd need to rearrange as x = f(y).

Q4: How accurate are the results?
A: Results use numerical integration for high accuracy, typically within 6 decimal places.

Q5: What about the washer method?
A: For hollow volumes, subtract inner function: π∫[f(x)² - g(x)²]dx.