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anonymous
 5 years ago
Please solve this discs problem:
Let R be the region bounded by the graphs of y=1/ sqroot of x,x=3.5 , and y= 4.6.
Find the volume generated when region R is rotated about the vertical line x=3.5.
(anwser at least three places after the decimal)
anonymous
 5 years ago
Please solve this discs problem: Let R be the region bounded by the graphs of y=1/ sqroot of x,x=3.5 , and y= 4.6. Find the volume generated when region R is rotated about the vertical line x=3.5. (anwser at least three places after the decimal)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0My approach is this: you can only do this kind of volume problem by rotating around the xaxis or the yaxis. Since they gave you an "offaxis" rotation, begin by moving the given axis TO the yaxis (since the axis is vertical). That's a move of 3.5 units to the left. A move of 3.5 units to the left is accomplished by subtracting 3.5 from x wherever we find x. In this case, y=1/sqrt(x) becomes y=1/sqrt(x+3.5) and x=3.5 becomes x+3.5 = 3.5 or x=0. Moving the axis of rotation, and then moving all of the boundaries, gives you new equations but a simpler problem. You're now rotating a region about the yaxis. The volume of a disk is pi*r^2*thickness. The r is x (because the disks lie horizontally) and the thickness is dy (same reason). Since we can't mix x's and y's in the integral, solve the y equation for x. That's easily done. Now just plug into the pi*r^2*dy equation to get the thickness of one disk. To finish, integrate what you just created from the bottom y boundary to the top y boundary. I leave it to you to find the boundaries and finish up. The volume of a disk is pi*r^2*thickness.
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