Calculus - Math
posted by Sarah
Sorry in advance - it's a very wordy, multi part question. The parts with the ..........are the parts that require an answer. I have no idea where to begin or what to do to solve this.
We will determine the volume obtained when revolving the solid bound by the curves y = x^2 and y = 6x - 8 about the x-axis. Since these curves are expressed in terms of x, we will use the method of washers. First, we must find the intersection points of these two curves. These particular curves intersect at two points. If we call the smaller of these points x = a, and the larger point x = b, then the value of a is..........., and the value of b is............Between these two points, the curve that takes on smaller values is y1 = ................and the curve that takes on the larger value is y2 = ................Let us look at a typical washer. If we take a thin vertical slice of width dx, the volume of this slice can be expressed as follows: dV = piR^2 - pir^2, where R is the radius of the outside of the washer, and r is the radius of the inside of the washer. In this case, the outer radius is determined by the larger function, y2, and the inner radius is determined by the smaller function y1. Thus we have dV = pi(y2^2 - y1^2). We must then consider all such slices that are included in our region. Thus we have to integrate from a to b. Thus the integral used to calculate the volume is integral from b to a...................dx (enter the function which you will be integrating in terms of x). Therefore the volume is..................
Thanks for your help.
They are trying to make it easy for you, going though the process step by step.
You really need to make the effort.
For the first step, set
x^2 = 6x - 8 and solve for the two x values.
x^2 -6x +8 = 0 can be easily factored.