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benedwards2020
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Find the volume of the solid of revolution obtained when the region under the graph of
[tex]f(x) = \left( \frac{1}{x} \right) e^\frac{1}{x} [/tex]
from x = 1 to x = 6
[tex] \pi \int (f(x))^2 dx [/tex]
Ok, the equation I gave above should be that of a definite integral with a=1 and b=6 (If anyone can tell me how to write that in Latex it would be much appreciated)
So, the volume is
[tex]\pi \int_1^6 \left( \frac{1}{x} \right) \left( e^\frac{1}{x} \right)^2 dx[/tex]
So, we can simplyfy this to
[tex]\pi \int_1^6 (x)^{-2} \times e^\frac{2}{x} dx[/tex]
Now I'm a bit stuck as to where to go from here. Do I use the integration by parts method? I think I'm getting bogged down in unnecessary calculations. Can someone give me a hint or point me in the right direction?
[tex]f(x) = \left( \frac{1}{x} \right) e^\frac{1}{x} [/tex]
from x = 1 to x = 6
Homework Equations
[tex] \pi \int (f(x))^2 dx [/tex]
The Attempt at a Solution
Ok, the equation I gave above should be that of a definite integral with a=1 and b=6 (If anyone can tell me how to write that in Latex it would be much appreciated)
So, the volume is
[tex]\pi \int_1^6 \left( \frac{1}{x} \right) \left( e^\frac{1}{x} \right)^2 dx[/tex]
So, we can simplyfy this to
[tex]\pi \int_1^6 (x)^{-2} \times e^\frac{2}{x} dx[/tex]
Now I'm a bit stuck as to where to go from here. Do I use the integration by parts method? I think I'm getting bogged down in unnecessary calculations. Can someone give me a hint or point me in the right direction?
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