The region in the first quadrant bounded by the graphs of and is rotated around the line Find the centroid of the region and the volume of the solid of revolution.
Rotate the coordinate axes .
The transformation will make a new graph.
Now simplify find the volume of the region around the x-axis.
(I will do this problem latter. Right now I am using one of my many computers. This one does not have a gprahing program.)
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You have,
this describes your curve.
From conics you should be familar that a rotation of transforms,
Equivalently,
Thus,
Thus,
Now the problem is that this curve is not a function (if I only had a graph) and the shell formula needs to curve to be a function. So I am going to divide this curve into two curves that are functions and add their rotational volume about the y-axis. In order to do that I will first need to bring this to the form . To do that I need to solve for .
First rewrite as,
Thus,
(TO BE CONTINUED)
Well, since you asked. I am taking a cracker-jack on-line Calc I class. This is the last question on an open-book test. I have answered the others, some with the help of this forum. I am averaging a whopping 72% in the class, and passing is all I care about right now Anyway, I can't really afford to leave this one blank, the adjunct usually gives partial credit for at least getting part of it right!