Improper integral Definition and 236 Threads

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Regarding the integral from -infinity to 0 of 6/(5x-2) --> I arrive at 6/5*ln(u), is this the right thing? How would I evaluate something like ln(-2), or do I just assume it is divergent since it the other limit will come out to neg infinity?

For the integral from 0 to infinity of xe^(-5x)dx... I am getting as far as: -1/5*x*e^(-5x) + 1/5*int of (e^(-5x)dx) But I am getting stuck at this point. We are supposed to come out with 1/25 for the answer but how would I evaluate the "-1/5*x*e^(-5x)" since that is already out of...

evaluate \int_0^{33} {\left( {x - 1} \right)^{ - 1/5} } \,dx The back of the book gives 75/4 as the answer. I get 80/4. It has an asymptote at 1 since 0^(-1/5) DNE, and 0.00000001^(1/5) equals a number that grows larger as I add more 0's. But any time I try to raise a negative number...

the SM shows a different method but i figure i should arrive at the same answer either way. what step am i screwing up on? thanks! \int_{ - \infty}^{\infty}\frac {x^{2}dx}{9 + x^6} \int_{ - \infty}^{0}\frac {x^{2}dx}{9 + x^6} + \int_{0}^{\infty}\frac {x^{2}dx}{9 + x^6} u = x^{3} du =...

Ok, my book has the example int from -1 to 2 of dx/x^3 this gets split into int from -1 to 0 of dx/x^3 and int from 0 to 2 of dx/x^3. Now, he had previously determined that the second integral returned positive infinity (diverges) by taking the lim as b approaches 0+. So, the book...

Homework Statement Discuss the convergence of the integral 1/[x^2 + y^2 + z^2 + 1]^2 dxdydz in the whole space. Homework Equations The Attempt at a Solution Since the space is unbounded, the integral is an improper integral so we can consider a sphere with radius N and take...

Hie, I have attempted the following inproper intergral, and I just wanted to check that I have answered it the correctly, if not, any tips would be great. I attached them as pics. I attached my steps as pics, as I am not sure how to writ ein text on these forums. My answer is thus = 0...

Hi, I'm having a bit of trouble showing that the integral from 1 to infinity of x/((1+x^6))^1/2 converges or diverges by the comparative property. I'm not sure if I'm setting it up right, but so far I have that 1/rad(1+x^6) is less than or equal to x/rad(1+x^6) which is less than 1/rad(x^6)...

\int \frac{dx}{x \sqrt{x^2-4}} there are bounds to this problem but it is irrelevant since my problem is with the integration and not finding the limits. this integral resembles that of arcsec(x) but I am not sure how to deal with the -4. is there any way to solve this with partial...

Hello, I just finished up two problems for my homework and I have a sneaking notion that I have made a mistake somewhere because when I checked the answer numerically by calculator and I get a differing number. I'm doing improper integrals for my real analysis class and the problem is stated...

hi, why is ln|x|, from -1 to 1, converging? is "0" the bad point, and must i break up the integral from 1 to $, where $ = 0, and from $ to -1... so i have xlnx-x as my derivative... and i get -2? thanks

Why does lim(t-->-infinit) (1/3)e^(-t^3)=0? or is it -infinit? I'm lost.

basically I'm stuck with this problem... Integral the upper limit is positive infinite and the lower limit is 1 X/(sqrt(1+x^6) dx... can someone give me an idea on how to start this?...I really don't know. Thanks.

Improper integral and "rectangle" method If we have a definite integral then..using "rectangle" method we can get the approximation: \int_{a}^{b}f(x)dx \sim \sum_{n=0}^{N}f(a+nh)h My question is..how do you define this method when b-->oo (Imporper integral?)...:confused: :confused:

Hi, for some reason I can't remember and I've been looking everywhere for some info but can't find anything. I am trying to find out the answer to : \int_1^i^n^f^i^n^i^t^e \frac{1}{(3x+1)^2}dx what is the integral of \int \frac{dx}{(ax+b)^2}? Thanks

I was doing a Fourier Transform Integral, and was wondering if it would be legitimate for me to choose a semicircle C[SIZE="2"]R on the lower half-plane below the real axis rather than choosing a semicircle C[SIZE="2"]R on the upper half-plane above the real axis. I would expect it to be valid...

\int_{-\infty}^{\infty} e^{-|x|} dx Could someone tell me why this integral, when you split it comes out to be: \int_{-\infty}^0 e^x dx + \int_0^{\infty} e^{-x} dx I keep thinking it should be e^(-x) in the first integral. I don't know why its positive. I can solve this integral...

I am a physicist, not a mathematician. This problem has bothered me for 40 years. All introductory Calculus texts would consider this integral divergent. An example found in many texts is the integral of 1/(x-2) from 0 to 3, which is just a variant to the question I am asking. What I find...

Int[(x^3)/((e^x)-1)] [0, infinity] What is the trick? I thought of by-parts but how would you integrate 1/((e^x)-1)? Substitution won't work with u = e^x -1 with x = ln|u+1| or it would be rather tough to evaluate u^3 Someone please give me a hint.

I'm trying to find \int\limits_0^{ + \infty } {\frac{{\sin x}} {{x^3 + x}}dx} Since the function is even, I can compute it as \frac{1} {2}\int\limits_{ - \infty }^{ + \infty } {\frac{{\sin x}} {{x^3 + x}}dx} To use the residue theorem, I construct a large semi-circle C with center O and...

Can someone explain why the following improper integral diverges? Integral 1/x dx from -1 to 1 I know if you break it up the individual integrals (from -1 to 0 and 0 to 1) diverge to negative infinity and infinity, whose sum is indeterminant in general, but the symmetry of the integral...

Can you please offer any hints or suggestions on how to do these two problems: 1) Find the Maclaurin series of (x^2 + 1)/(3x^2 + 2x - 1). Should I perform long-division first? I can't seem to find any repeating pattern... 2) Evaluate the integral sqrt(12-4x-x^2) from x=2 to x=6. I...

I have to analize the convergence of the following integral: \int_0^1 \frac {x^2+1} {\sqrt x * (1-x)^{5/4}} I tried to divide it between 0-1/2 and 1/2-1 and on the first one i reached to: \int_0^{1/2} \frac {x^2+1} {\sqrt x * (1-x)^{5/4}}<=\int_0^{1/2} \frac {x^2+1} {x^{14/4}} can i say...

I've posted on Homeworks one of the number I did not understand. However, I would like to know the steps to calculate an improper integral of type 2. The type 2 is the one from constant a to constat b, not the one with inifnite. Please tell me the steps the accomplish it. :smile: I know...

Proving an indeterminate form Prove for all positive integers n that \lim_{x\rightarrow 0}x({lnx})^n=0 Thanks for any help.

Evaluate the integral: \int^{\infty}_{0}\frac{x\arctan{x}}{(1+x^2)^2}dx can anybody give me some hint? :cry: Thanks in advance

I was wondering. When is the following legal? \frac{\partial}{\partial y}\int_{-\infty}^{\+\infty}f(x,y)dx=\int_{-\infty}^{\+\infty}\frac{\partial f(x,y)}{\partial y}dx I know the rule when the limits of integration are bounded, but here there are four limits involved. One for the...

Does this improper integral converge? I have an interesting problem that has been bothering me. Given: f(x)=1/x g(x)= (any continuous, non-negative function) g(x)<f(x) A = (a positive constant) I want to know: Does the integral of g(x) from A to +infinity converge? Or...

I need to find a function f(x), if one exists, such that: lim (x->inf) x^2*f(x) = 0 And the improper integral of f(x) from 1 to infinity doesn't exist. I'm thinking that no function can satisfy these requirements, but apparently I'm wrong... help anyone?

I can't seem to evaluate integrals with infinite limits as well as improper integrals. Can anyone help in that? Sorry if this is a little vague but I'm stumped by the whole topic !

I stopped at the last step while calculating this improper integral: integral of x^3\ ( x^4 - 3)^1\2 with limits from 1 to infinity... that's x cubed over the square root of x raised to 4 minus 3... after replacing infinity with b and taking the limits it seems that I have to take...

OK, so I'm trying to work out this: \int^{\infty}_a \frac{\dx}{x} Where a is a positive constant. Can you evaluate this analytically? I'm thinking the limit must exist, but \ln \left( \infty \right) = \infty , or at least tends to it in the limit. So can someone tell me the deal...

How do I do \int_{3}^{6} (5-x)^{\frac{-1}{3}} \,dx ? I also need to know how to do \lim_{t\rightarrow\infty} \int_{-t}^{t} \frac{x}{x^2 + 1} \,dx