Improper integral Definition and 238 Threads

Homework Statement f(x) is a continuous and positive function when x\in[0,\infty). (#1) x_n is a monotonic increasing sequence, x_0=0 ,x_n \rightarrow \infty. (#2) Prove or contradict: \mbox{If } \sum_{n=0}^\infty \int_{x_n}^{x_(n+1)} f(x)dx \mbox{ is convergent (#3) then }...

[PLAIN]http://estro.uuuq.com/_proof.jpg I think I miss something...

Homework Statement evaluate \int \frac{1}{(1+x)\sqrt{x}} dx Homework Equations N/A The Attempt at a Solution how to do this, i can't use partial fraction, and integration by part makes it harder i guess, maybe using substitution, but how T_T helpp

Homework Statement Let [a, b) be an interval in the reals, with -\infty < a < b \leq \infty , and let \alpha: [a,b) \to \mathbb{R} be monotone increasing. Suppose that f: [a,b) \to \mathbb{R} is a function such that for each c \in (a,b) , f is integrable over [a,c ] with respect to...

Homework Statement Solve the integral \int\frac{1}{\sqrt[3]{x-1}}. Upper limit of integration is 1 while lower limit is 0. Homework Equations N/A. The Attempt at a Solution The only thing that I'm sure about is that the antiderivative of the integral is \frac{3}{2}(x-1)^(2/3) +...

Homework Statement integral of sech(x) from -Inf to Inf using residues. Homework Equations Calculate using: (2 Pi I) * Res[sech(x), "poles in upper half plane"] The Attempt at a Solution I used sech(x) = 2/[exp(x)+exp(-x)] to find a simple pole at z = (I Pi)/2 with a residue of -I. Then...

Hello-- I have a function: u(t,\tau)=\frac{1}{\pi}\int_{0}^{\infty}\! G(\omega)\, d\omega G(\omega)=4\sqrt{\pi}\frac{\omega^{2}}{\omega_{0}^{3}}\mbox{exp}\left(-\frac{\omega^{2}}{\omega_{0}^{2}}\right)\mbox{cos\left(\omega...

Homework Statement Homework Equations The Attempt at a Solution I'm trying to rewrite the integral as shown Most probably a real simple answer Thank you

Hello-- I need to generate synthetic data to test an algorithm used to process data from an experiment. A synthetic wavelet is constructed using the following equations, but I am uncertain how to numerically evaluate the improper integral shown below. \[ u(t) = {\mathop{\rm...

Homework Statement Using the fact that the integral from -Infinity to Infinity of e^-x^2 is equal to Sqrt(Pi), find the integral from -Infinity to Infinity of x^2 * e^-x^2 Homework Equations The Attempt at a Solution I really don't know how to find this using the fact that...

Homework Statement By rotating R=$\{ (x,y)|x\geq0, 0\leq y\leq \frac{1}{0.6 x+1.7}\}$ about the x-axis we obtain a solid with the volume V = ______ Homework Equations The Attempt at a Solution $\int _0^{\infty }\frac{dx}{0.6 x+1.7}$ is divergent but what do i do to get the volume? if don't...

Homework Statement I am to determine whether the following integral is convergent or divergent \int_0^1 \frac{sin(x)}{x} From what I hear since, lower limit is zero there is a removable discontinuity. Thus just because of this, it is convergent? Can someone let me know if this is correct.

Homework Statement \int(2dx/(x^2+4) from x= -\infty to x=2 Homework Equations No specific ones. The Attempt at a Solution So, from there I tried to split the integral into two, integrating between 2 and -2, and -2 and -\infty, but I got very lost trying to take the limits for these, partly...

How the following limit can be zero, since after applying L'Hospital rule the root x will be in the numerator, which together with sinx will constitute infinity.

Homework Statement Use Comparison Theorem to determine whether the integral is convergent or divergent: integral from 0 to infinity of: arctan(x) / (2 + e^x) Should look like this: http://bit.ly/cAhytV Homework Equations -- The Attempt at a Solution I tried to compare...

[Solved] Improper Integral Integration Sorry, don't know how to use the latex stuff for integrals :P Homework Statement Integrate the following from 0 to infinity: 1/(sqrt[x]*(1+x)) Homework Equations Integrate 0 to 1: 1/(sqrt[x]*(1+x)) Integrate from 1 to infinity...

Homework Statement Use a comparison to determine if the improper integral converges or diverges. If the integral converges, give an upper bound for the value. Integral of d(theta) / (theta^3 + theta)^1/2 from 1 to infinity Homework Equations N/A The Attempt at a Solution I'm...

Homework Statement \int_{-\infty}^{\infty} e^{x\over 2}e^{-x^2\over 2} dx Homework Equations \int_{-\infty}^{\infty}e^{-x^2\over a} dx = \sqrt{\pi\over a} a>0 The Attempt at a Solution Can't seem to penetrate it, I thought about trying to isolate the second term with...

Homework Statement \int_{-3}^{1}\frac{x}{\sqrt{9-x^{2}}} Homework Equations Let f be continuous on the half-open interval (a, b] and suppose that \lim_{x \to a^{+}} |f(x)| = \infty. Then \int_{a}^{b}f(x) dx = \lim_{ t \to a^{+}}\int_{t}^{b}f(x) dx The Attempt at a Solution...

if you use the limit comp test to show a polynomial behaves like it's highest powered term and that term has a negitive coefficient can the test still be used but with abs vals

Is there any way to integrate \int dx/(xlogx) within the limits 1 and n? If yes what is the result?

\int_{-1}^1 \frac{dx}{x} = \lim_{a \rightarrow 0} \int_{-1}^a \frac{dx}{x} + \int_a^1 \frac{dx}{x} = 0 . Since 2a also goes to 0 for 'a' going to 0, then we have \int_{-1}^1 \frac{dx}{x} = \lim_{a \rightarrow 0} \int_{-1}^{2a} \frac{dx}{x} + \int_a^1 \frac{dx}{x} = ln2. It seems like...

Homework Statement Find: \int_{0}^\infty \frac{\sqrt[3]{x}-\sqrt{x}}{x^b+a^b}dx With x>0 and a>2. Homework Equations The Attempt at a Solution I think it's probably something with Beta, but I'm not sure how to change it into the proper form. I thought changing it into: \int_{0}^\infty...

Hey guys, I was doing some homework problems and I ran into a problem regarding how to solve a certain improper integral. \int e^{t*(b-s)} evaluated from 0 to \infty So I take the integral and get \frac{\int e^{t*(b-s)}}{-(b-s)} which evaluated from 0 to \infty gives me 0 -...

Establish convergence/divergence of the following improper integral: integral from 0 to infinity of 1 / ( x^(1/3)*(/x-5/^(1/3))*(1 + sqrt(x))^0.7) ) My attempt at a solution was to break it up into 3 intergrals: 0 to 1, 1 to 5, and 5 to infinity...I showed that the first two of these...

With the help of F:[0-> infinity) F(t)= S( (e^(-tx)) sin(2x)/x )dx find the S sin(2x)/x dx . The integral goes from 0 to infinity.

Homework Statement AN object moving along a curve in the xy-plane is at position (x(t),y(t)) at time t, where dx/dt=Arcsin(1-2*e^(-t)) and dy/dt= 4t/(1+t^3) for t>or= 0. At time t=2, the object is at the point (6,-3). a. Let m(t) denote the slope of the line tangent to the curve at...

Homework Statement The integral from -infinity to infinity of (2-x^4)dv Homework Equations U substitution The Attempt at a Solution Dont know what to use as my "u" ? Can someone please help me out? Thank you in advance.

given the improper integral from 0 to 1 of \intdx/\sqrt[3]{x}(ee-e-x) i am asked if it comverges or diverges, what i have learned is that if i can find : -a similar function that is bigger than my function and that i know converges, then my function also converges -a similar function...

Homework Statement integral from 2 to infinty 1/(x-sqrt(x)) The Attempt at a Solution my teacher wants us to compare it to another function in the form 1/x^p and not integrate it so would i compare it to 1/x and then do the limit comparison test limit as x approaches infinity...

Homework Statement Prove that \lim_{x \rightarrow \infty} exp(-x^2) \int_0^x exp(t^2) dt = 0 . Homework Equations The Attempt at a Solution This question is giving me a lot of difficulty. I've tried a lot of different ways to do it, here is a list of ways that I've tried...

Homework Statement Prove that \int_0^{\infty} sin^2(\pi(x + 1/x))dx does not exist.Homework Equations The Attempt at a SolutionFirst, we can construct a sequence as follows: \int_0^{\infty} f(x)dx = \lim_{n \rightarrow \infty} S_n , where S_n =\int_0^{1} f(x)dx, \int_0^{2} f(x)dx...

Homework Statement Integral from negative infinity to positive infinity of (1/(sqrt(1+x^2))dx 2. The attempt at a solution Using trig substitution I got the integral equal to ln|sqrt(1+x^2) + x| Finding this was not the difficult part. Evaluating it is. I set it up like this: lim b -->...

Homework Statement I'm trying to show that this improper integral converges \int_{0}^{1} \sin \left ( x + \frac{1}{x} \right )dxHomework Equations The Attempt at a Solution I thought a comparison test would be nice but I can't think of the right one if that is the way to go. I don't think a...

Homework Statement integral from -1 to 1 of 3/x^2 dx Homework Equations The Attempt at a Solution Limit t --> infinity integral from -1 to t of 3/x^2 dx + limit t --> infinity integral from t to 1 of 3/x^2 dx Limit t-> infinity -3/t - (-3/-1) + Limit t-->...

Homework Statement Determine if the integral converges or diverges? it;s the integral of 0 to infinity of 1/(1+x^6)^(1/2) Homework Equations so I compared it with 1/x^2 The Attempt at a Solution the answer key says it converges but i think it diverges since the integral of 1/x^2...

Hello and Happy New year, I'm having some trouble computing this integral: limn->00\int^{1}_{0}\sqrt[3]{1+x^{n}sin(nx)} Any suggestions are appreciated.

Homework Statement integral of x*e^x from 0 to infinity Homework Equations N/a The Attempt at a Solution i first integrated the integrand and got (xe^x - e^x) then i use limit as R approaches infinity and used 0 and R as my limits. when calculating i keep getting 1 instead of...

1. Let F(x)= \int^{x}_{0} \frac{sint}{t} and f(x) = \frac{sinx}{x}. If x approaches infinity, F(x) approaches \pi/2. So, Explain what does this mean for the improper integral \int^{\infty}_{o}\frac{sinx}{x} Homework Equations Explain what does this mean for the improper integral...

Homework Statement integral (from 0 to 1) of (lnx)dx/(x^0.5) Homework Equations I did u-substitution and got the antiderivative to be 4ln(sqrt(x)) - 4sqrt(x) The Attempt at a Solution The answer that I got was that the limit of the antiderivative (as t approaches 0 from the...

Homework Statement Hey. I'm kinda stuck on this one, any idea? Homework Equations The Attempt at a Solution

Homework Statement i was deriving an infinite line of charge formula by coloumb's law: so i got stuck with this integral (since it is in the maths forum) \vec{E}_{\rho} = \int_{-\infty}^{\infty} \frac{\rho_L \rho dz}{4\pi\epsilon_o ({\rho}^2 + z^2)^{\frac{3}{2}}} Homework Equations where...

\int_0^\infty \; \frac{ \ln\;(1+x^2)}{ x^2+2x\;\cos\;\theta + 1 }\;\;dx \theta \in \mathbb{R}

This was a problem on one of my previous tests that I got wrong entirely. In preparing for my final, I'm attempting to redo it. I was wondering if someone could check my work. Determine whether the following improper integral is convergent or divergent. If the integeral is convergent, find its...

Let A be a constant. Let f(t) be an integrable function in any interval. Let h(t) be defined on [0, oo[ such that h(0) = 0 and for any other "t", h(t) = (1 - cos(At)) / t It is not difficult to see that h is integrable on [0, b] for any positive "b", so fh is also integrable in...

Homework Statement Evaluate the integral: \int\frac{dx}{x^{3}+x^{2}+x+1} from infinity to zero Homework Equations lim t--> infinity [/tex] \int \frac{dx}{x^{3}+x^{2}+x+1} The Attempt at a Solution lim t-->infinity [/tex] \int \frac{dx}{(x+1)(x^{2}+1} I'm stuck on where to go...

Could anyone please explain how to solve the improper integral below? I have no idea of how to do it. If f is a bounded non-negative function, then show that the integral from zero to infinity of f(x+1/x)*ln(x)/x dx=0. Thank you.

Improper Integral [Solved] Homework Statement \int_{0}^{\infty} (x-1)e^{-x}dx Homework Equations Integration by Parts Improper Integrals The Attempt at a Solution \lim_{R\rightarrow \infty} \int_0^R~xe^{-x}-e^{-x}dx Let u = x du = dx Let dv = e^-x...

Homework Statement Show \mathop{\lim}\limits_{n \to \infty}(\frac{1}{n!}\int_{1}^{\infty}x^n\frac{1}{e^x} dx )=1 Homework Equations The hint is that e=\mathop{\lim}\limits_{n \to \infty}\sum_{k=0}^{n}1/k! The Attempt at a Solution First I wrote out the improper integral as limit...

Homework Statement Does the integral from 0 to Infinity of \int\frac{1}{\sqrt x \sqrt{x+1}\sqrt{x+2}}dx converge or diverge?Homework Equations None.The Attempt at a Solution I tried to integrate it, but I haven't even been able to do that so I couldn't then evaluate the limit of the...