1. What is the Disk Method Volume Calculator?

Definition: This calculator computes the volume of a solid of revolution using the disk method in calculus.

Purpose: It helps students and professionals determine volumes of rotated solids about the x-axis.

2. How Does the Calculator 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.

3. Importance of Volume Calculation

Details: The disk method is fundamental in calculus for finding volumes of complex shapes in engineering and physics.

4. Using the Calculator

Tips: Enter the function f(x) (e.g., "x^2", "sin(x)"), integration limits (a must be less than b).

5. Frequently Asked Questions (FAQ)

Q1: What types of functions can I enter?
A: The calculator supports polynomial, trigonometric, exponential, and logarithmic functions.

Q2: What if my function has vertical asymptotes?
A: The integral may not converge. Ensure your function is continuous on [a,b].

Q3: Can I rotate around the y-axis instead?
A: For y-axis rotation, use the shell method instead of the disk method.

Q4: How accurate are the results?
A: Results are numerically approximated but typically accurate to several decimal places.

Q5: What if I get an error message?
A: Check your function syntax and ensure lower limit is less than upper limit.