1. What is a Volume with Integral Calculator?

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

Purpose: It helps students and professionals calculate volumes formed by rotating a function around the x-axis.

2. How Does the Calculator Work?

The calculator uses the 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 integral sums up infinitely many circular disks with radius \( f(x) \) along the x-axis from \( a \) to \( b \).

3. Importance of Volume Calculation

Details: This method is fundamental in calculus and has applications in physics, engineering, and 3D modeling.

4. Using the Calculator

Tips: Enter a valid mathematical function (e.g., "x^2", "sin(x)", "sqrt(x)"), and integration limits where \( a < b \).

5. Frequently Asked Questions (FAQ)

Q1: What types of functions can I use?
A: Most standard mathematical functions are supported (polynomials, trigonometric, exponential, etc.).

Q2: What if my function has vertical asymptotes?
A: The integral may not converge if the function is undefined or infinite within the interval.

Q3: Can I use this for rotation around the y-axis?
A: No, this calculator uses the disk method for x-axis rotation only.

Q4: How accurate are the results?
A: Accuracy depends on the numerical integration method used (implementation dependent).

Q5: What's the difference between disk and shell methods?
A: Disk method uses circular slices perpendicular to the axis, while shell method uses cylindrical shells parallel to the axis.