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irony of truth
Sep22-04, 09:19 AM
I am performing the numerical integration of finding the area of 1/x dx from 0 to 2... using Simpson's rule of n = 6. What will I do in this problem like this since 0 to be evaluated in the f(x) = 1/x is undefined?
matt grime
Sep22-04, 09:28 AM
I'd check the question since the integral doesn't exist.
JasonRox
Sep22-04, 09:12 PM
I'm sure it does.
The integral(anti-derivative) is ln x.
I'm pretty darn confident that's what it is. I'd prove it, but I'm not in the mood to spend time on here, and last time I tried Latex it didn't work.
y = ln x
dy/dx = 1/x
mathwonk
Sep22-04, 09:19 PM
if you are so concerned about your time why are you wasting ours?
I'm sure it does.
The integral(anti-derivative) is ln x.
I'm pretty darn confident that's what it is. I'd prove it, but I'm not in the mood to spend time on here, and last time I tried Latex it didn't work.
y = ln x
dy/dx = 1/x
Yes, but what is the value of ln(x) when x = 0? Even if you try to avoid that limit of integration your answer will diverge as you move your endpoint closer to x = 0.
matt grime
Sep23-04, 04:46 AM
the integral, as an improper riemann integral (limit h to zero of int from h to 2) does not exist, Jason. The function has an antiderivative, and that can be used to prove this fact.
JasonRox
Sep23-04, 02:17 PM
if you are so concerned about your time why are you wasting ours?
Relative to me, your time is going slow, so you might as well take advantage of it. :biggrin:
Kidding.
Sorry, I was getting ready to go to bed, and Latex in fact didn't work last time.
Should of checked my answer, and yes it is wrong.
metacristi
Sep25-04, 03:02 AM
I am performing the numerical integration of finding the area of 1/x dx from 0 to 2... using Simpson's rule of n = 6. What will I do in this problem like this since 0 to be evaluated in the f(x) = 1/x is undefined?
You can still use Simpson method,though the integral is improper,by taking the limits of the integral as being from 'a' to 2 (where 'a' tends to 0).Finally take the limit for a->0 from the expression in 'a' obtained after applying Simpson's method.The results is ∞,the integral diverges.
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