You have the right idea! Keep in mind, though, that the horizontal refers to values of y, not x. So you would take the top curve , square it, and subtract it from the square of the lower curve
Is it clearer now on why the volume [using the washer method] would be ?
--Chris
Okay, I think I understand where you're coming from. What do you mean exactly when you said, "that the horizontal refers to values of y, not x." So when I have a problem that says rotate about the y axis, the limits are referring to y correct? But what about something like this:
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
about the y-axis
So would I use the washer method and integrate from 0 to 1?
According to your graph, the horizontal values were the y values. Otherwise it would look like this if you were looking at it from the standard cartesian system:
Get these in terms of y:So when I have a problem that says rotate about the y axis, the limits are referring to y correct? But what about something like this:
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
about the y-axis
So would I use the washer method and integrate from 0 to 1?
So, in terms of y, and , and its being integrated from 0 to 9. [Since at x=3, y=9]
So the integral here would be
Does this make sense?
--Chris
Yea, I think so, so you subtract because you do the right function minus the left and square both. But how will it look on a graph, what portion gets thrown around. I couldn't figure out how to plot a straight line for x=3 so I just drew it in photoshop.
The light green shaded region is what were are dealing with here:
Since we graphed the functions as , the horizontal here represents the y axis and the vertical represents the x axis.
So here, we have the top function as , and the bottom function is . These two functions intersect at
Since we are revolving it about the y axis [horizontal], our volume integral would be
Does this make sense?
--Chris