Hi,
I have a problem i wasn't able to solve, i don't know how to calculate the volume of the generated body, when it is rotated around both the x and the y axis.
Jones
I can show you how to calculate the volume when the curve rotates about the x-axis.
The general formula for a rotation volume with the x-axis as axis of rotation is:
Plug in the terms you know:
Now use integration by substitution:
The integral becomes:
Can you take it from here?
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There is missing at least one value to calculate the rotation volume if the y-axis is the axis of rotation.
I've had some difficulties to understand this line:
If you mean
then the property is unnecessary because f(1) = e < 3.
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To calculate the rotation volume with the y-axis as axis of rotation you have to use the general equation:
Since
this equation becomes:
But unfortunately the integrand becomes very ugly so I can only provide you with an approximative result: