Find the volume of the solid formed when the region is revolved around the y-axis.
To find the volume of the solid formed when the region is revolved around the y-axis, we can use the method of cylindrical shells.
Let's say the region is bounded by the curves y = f(x), the x-axis, and the lines x = a and x = b. The volume V of the solid formed by revolving this region around the y-axis is given by the integral:
V = ∫[a,b] 2πx*f(x) dx
This formula can be derived from considering the volume of a cylindrical shell at each x-value in the region.
We first need to find the function f(x) that represents the curve bounding the region. Once we have found f(x), we can determine the limits of integration a and b.
Finally, we can evaluate the integral to find the volume of the solid formed when the region is revolved around the y-axis.