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MrShickadance
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Homework Statement
f(x) = 1/x
Interval [1, ∞) about the x-axis
Set-up the integral for the surface area of the solid
Then use the substitution u = x2 and integrate using the formula:
∫ sqrt(u2 + a2) / u2 du = ln(u + sqrt(u2 + a2) - sqrt(u2 + a2) / u + C
a is a constant
Homework Equations
S = 2pi * ∫ (f(x) * sqrt(1 + [f`(x)]2) dx from a to b
The Attempt at a Solution
First, I found the derivative of (1/x) which is -1/x2
I then plugged f(x) and f`(x) into the surface area equation
I squared f`(x) to get (1/x4)
My equation is 2pi ∫ (1/x) * sqrt(1 + (1/x4) from 1 to infinity of course, which I will change to the limit as b approaches infinity because it is an improper integral.
I simplified the fractions under the radical to get sqrt((x4 + 1) / x4)
I took the square root of the denominator to get x2
Lastly, I multiplied (1/x) by sqrt(x4 + 1) / x2 to get
sqrt(x4 + 1) / x3
If u = x2 then this is not in the correct form to use the formula that was given to me.
How can I get the denominator to equal x4?
I will figure out the rest of the problem from there.
Here is my written attempt:
Thanks!
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