Respuesta :
The first thing you need to do is find the intersection of the two curves on the plane.
You will want only the overlapping area of your curves in the washer so you need to decide which of the curve will be the upper or lower boundary - (which one you will need to subtract from the other).
You can make this process easier by looking at the x plane or the y plane only of the curve - Caution! if you look at the y plane you will have to switch the function to be in terms of y and your limits of integration will need to change too!
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From there you can find limits of the washer for the x or y axis.
To find your volume your going to want to have defined the cross area with your function and then multiply it by dx (or dy, depending on which axis your revolving the washer)
Then you can use a definite integral (using the limits you found earlier) and integrate it to find the volume of that washer.
Its a little difficult to explain the process because it helps to look at a 3d image. Those are the basic steps for solving the volume of a washer though.
You will want only the overlapping area of your curves in the washer so you need to decide which of the curve will be the upper or lower boundary - (which one you will need to subtract from the other).
You can make this process easier by looking at the x plane or the y plane only of the curve - Caution! if you look at the y plane you will have to switch the function to be in terms of y and your limits of integration will need to change too!
-
From there you can find limits of the washer for the x or y axis.
To find your volume your going to want to have defined the cross area with your function and then multiply it by dx (or dy, depending on which axis your revolving the washer)
Then you can use a definite integral (using the limits you found earlier) and integrate it to find the volume of that washer.
Its a little difficult to explain the process because it helps to look at a 3d image. Those are the basic steps for solving the volume of a washer though.
