1. What is the Disk Method for Volume of Revolution?

Definition: The disk method calculates the volume of a solid formed by rotating a function around an axis by integrating circular cross-sections.

Purpose: Used in calculus to find volumes of complex 3D shapes generated by rotating 2D functions.

2. How Does the Disk Method Work?

The calculator 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 to compute the total volume.

3. Importance of Volume of Revolution

Details: This concept is fundamental in engineering and physics for calculating volumes of objects with rotational symmetry.

4. Using the Calculator

Tips: Enter the function (e.g., "x^2", "sin(x)"), integration limits (a must be less than b). The calculator will numerically approximate the integral.

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 volumes.

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

Q3: What if my upper limit is less than lower limit?
A: The calculator will return an error - limits must satisfy a < b.

Q4: How accurate is the numerical integration?
A: The calculator uses precise numerical methods to approximate the integral.

Q5: Can I rotate around the y-axis instead?
A: This calculator handles x-axis rotation. For y-axis, you'd need to rearrange the function.