1. What is the Volume Calculator (Disk Method)?

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

Purpose: It helps students and professionals calculate volumes of complex shapes using integral calculus.

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 circular disks along the axis of rotation to calculate the total volume.

3. Importance of Volume Calculation

Details: The disk method is fundamental in engineering and physics for determining volumes of objects with rotational symmetry.

4. Using the Calculator

Tips: Enter the function in terms of x (e.g., "x^2", "sin(x)", "sqrt(x)"), the lower and upper limits of integration. The upper limit must be greater than the lower limit.

5. Frequently Asked Questions (FAQ)

Q1: What functions can I enter?
A: The calculator supports standard mathematical functions including polynomials, trigonometric, exponential, and logarithmic functions.

Q2: What if I get an error?
A: Check your function syntax and ensure the limits are valid (b > a). Avoid undefined points in your interval.

Q3: Can I use this for the washer method?
A: For washers (with a hole), you would need to subtract the inner radius squared from the outer radius squared in the integrand.

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

Q5: Can I rotate around the y-axis instead?
A: For y-axis rotation, you would need to use the shell method or express x as a function of y.