Numerical Integration: Simpson's Rule for 1/x

[irony of truth]

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]

I'd check the question since the integral doesn't exist.

 

[JasonRox]

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]

if you are so concerned about your time why are you wasting ours?

 

[Tide]

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]

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]

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.

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]

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.