The volume of a solid of revolution generated by rotating the function y = f(x) around the x-axis is calculated using the disk method which involves integrating the area of circular slices along the interval from x=a to x=b, confirming the formula V=π∫abf(x)2dx.
The volume of a solid of revolution generated by rotating a function y = f(x) around the x-axis can be understood by slicing the solid into infinitesimally thin disks perpendicular to the x-axis. Each disk's volume is the product of the area of its circular face, πf(x)2, and its infinitesimal width dx.
By integrating these volumes along the interval from x=a to x=b, we sum the volumes of all individual disks, leading to the formula V=π∫abf(x)2dx. This integral calculus method is known as the disk method in finding the volume of solids of revolution.
So, by applying integral calculus principles, specifically using the disk method, we obtain a mathematical model for calculating the volume of a solid of revolution around the x-axis, confirming the given formula V=π∫abf(x)2dx.