Final answer:
To find the volume of a solid formed by revolving a region bounded by a function f(x) and the x-axis around the y-axis, integrate π(f(x))^2 from the lower to the upper boundary of the interval. This is the disk method and the volume is found by the integral V = ∫₀ₐπ(f(x))^2dx.
Step-by-step explanation:
To find the volume of the solid generated by revolving a region bounded by a function f(x) and the x-axis on the interval [0, a] around the y-axis, we can use the disk method. If we consider a small slice of the region at a distance x from the y-axis with thickness dx, the area of the slice is π(f(x))^2. When this slice is revolved around the y-axis, it forms a disk with volume π(f(x))^2dx.
To find the total volume, we integrate this expression from x = 0 to x = a:
V = ∫₀ₐπ(f(x))^2dx
Without the specific function f(x), we cannot compute the exact volume, but this formula provides the general method to calculate the volume for a given f(x).
Remember, it's important to set up the integral carefully, taking into account the limits of integration and ensuring that the function describes the boundary of the region correctly for the method of disks.