1. What is the Disk Method in Calculus 2?

Definition: The disk method is a technique for finding the volume of a solid of revolution by integrating circular cross-sections perpendicular to the axis of rotation.

Purpose: It's used to calculate volumes of objects created by rotating a function around an axis, common in engineering and physics applications.

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
• \( \pi \) — Mathematical constant pi (~3.14159)

Explanation: The method sums up infinitely many thin disks with radius f(x) along the interval [a,b].

3. Importance of the Disk Method

Details: Essential for calculating volumes in engineering (tank design), physics (moment of inertia), and many real-world applications involving rotational symmetry.

4. Using the Calculator

Tips: Enter the function f(x) to rotate, the lower and upper limits of integration. The function should be continuous on [a,b].

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 by subtracting inner radius.

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

Q3: What about logarithmic or exponential functions?
A: Yes, use ln(x), log(x), exp(x) or e^x as needed.

Q4: How accurate are the results?
A: Results are numerically approximated but very precise for most practical purposes.

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