Need help with finding a volume of revolution with Cylindrical Shells method

y=2-0.5x, y=0, x=1, x=2, rotate about the x axis.
I know that it will be easier to solve it with the regular method, but I need it with cylindrical shell.
I cannot find the radius and the height.
The final answer is 19pi/12
Thanx

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Originally Posted by shaharg

y=2-0.5x, y=0, x=1, x=2, rotate about the x axis.
I know that it will be easier to solve it with the regular method, but I need it with cylindrical shell.
I cannot find the radius and the height.

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If you must use the shell method, you will need to set up two integrals: one for in which the height of each shell is simply 1, and then another for in which the height of each shell is

Quote:

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Originally Posted by Reckoner

If you must use the shell method, you will need to set up two integrals: one for in which the height of each shell is simply 1, and then another for in which the height of each shell is

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So, what is the radius and what is the height?

Quote:

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Originally Posted by shaharg

So, what is the radius and what is the height?

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I suggest drawing a picture. The average radius of each shell is the distance from the axis of rotation to each given -value. Since the axis of rotation is simply the -axis, this distance is given by The "height" of each shell (horizontal distance from side to side) I have explained in my previous post. It should be clear from looking at a picture.

Thank You