1. What is Volume of Revolution in Calculus 2?

Definition: This calculator computes the volume generated by rotating a function f(x) around the x-axis between limits a and b.

Purpose: It helps students and professionals solve problems in integral calculus related to volumes of solids of revolution.

2. How Does the Calculator Work?

The calculator uses the disk method formula:

Where:

• \( V \) — Volume of revolution (cubic units)
• \( f(x) \) — Function being rotated
• \( a \) — 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: Understanding volumes of revolution is fundamental in engineering, physics, and advanced mathematics for solving real-world problems involving 3D shapes.

4. Using the Calculator

Tips: Enter the function (e.g., "x^2", "sin(x)", "sqrt(x)"), integration limits (a must be less than b). The calculator supports standard mathematical notation.

5. Frequently Asked Questions (FAQ)

Q1: What functions can I input?
A: The calculator supports polynomials, trigonometric, exponential, and root functions (implementation would require a math parser).

Q2: How accurate are the results?
A: Results are numerically approximated but highly accurate for most educational purposes.

Q3: Can I use this for y-axis rotation?
A: This version calculates x-axis rotation only. A separate calculator would be needed for y-axis rotation.

Q4: What if my function has asymptotes?
A: The calculator would detect improper integrals and handle them appropriately (implementation required).

Q5: How is this different from shell method?
A: The disk method is used here. Shell method would require a different formula and calculator.