1. What is the Disk Method in Calculus?

Definition: The disk method is a technique for finding volumes of solids of revolution by integrating cross-sectional areas.

Purpose: It helps calculate volumes of objects created by rotating a function around an axis.

2. How Does the Disk Method Work?

The method uses the formula:

Where:

• \( V \) — Volume of the solid (cubic units)
• \( f(x) \) — Function being rotated
• \( a \) — Lower limit of integration
• \( b \) — Upper limit of integration

Explanation: The method sums up infinitely thin circular disks along the axis of rotation.

3. Importance of Volume Calculation

Details: Understanding volumes of revolution is fundamental in physics, engineering, and many applied mathematics fields.

4. Using the Calculator

Tips: Enter the function (e.g., "x^2", "sin(x)"), integration limits (b > a). The calculator will numerically approximate the volume.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between disk and washer methods?
A: The disk method is for solids without holes, while the washer method handles hollow solids.

Q2: Can I use trigonometric functions?
A: Yes, functions like sin(x), cos(x), etc. are supported.

Q3: What if my limits are reversed (a > b)?
A: The calculator will automatically handle this by taking the absolute value of the result.

Q4: How accurate is the numerical integration?
A: The calculator uses adaptive methods to provide accurate results for most functions.

Q5: Can I rotate around the y-axis instead?
A: This calculator handles x-axis rotation. For y-axis rotation, use the shell method instead.