This tool calculates the volume of a solid of revolution given a function and specific bounds.
How to Use the Solids of Revolution Calculator
To use this calculator, enter the function f(x) you want to revolve, the lower and upper bounds a and b, and the axis of revolution either ‘x’ or ‘y’. Click “Calculate” to get the volume of the solid formed by revolving the function around the specified axis.
Explanation of How It Works
This calculator uses numerical integration to approximate the volume of the solid formed by revolving a function around a specified axis. The function is broken into small intervals and the areas of these intervals are summed to approximate the total volume. For revolution around the x-axis, the function integrates π[f(y)]² dy from a to b. For revolution around the y-axis, it integrates π[f(x)]² dx from a to b.
Limitations
The accuracy of the result depends on the choice of the function and interval. Functions with rapid changes or discontinuities within the interval may lead to less accurate results. The calculator does not handle undefined points within the interval well. The result is an approximation, so for precise needs, consider using specialized tools or mathematical software.