Integrals Definition and 1000 Threads

I don't speak English very well, so it's very hard to me to explain my attemps to solve this problem, and I'm still learning to use latex, so it's so slow to me. I can scan my attemps if you want to see them. Homework Statement I_n = \int_{0}^{\infty} x^{2n-1}/(x^2+1)^{n+3} \dx, n \geq 1 I...

Homework Statement Im getting very confused with working out how to integrate the following double integral with an absolute value: \int^{2}_{-2}\int^{2}_{-2}\left|x^{2}+y^{2}-1\right|dxdy Homework Equations The Attempt at a Solution I know you have to split it down into where it...

Calculus: Coordinate Changes, Jacobian, Double Integrals?? Homework Statement Show that T(u,v) = (u2 - v2, 2uv) maps to the triangle = { (u,v) | 0 ≤ v ≤ u ≤ 3 } to the domain D, bounded by x=0, y=0, and y2 = 324 - 36x. Use T to calculate ∬sqrt(x2+y2) dxdy on the region D...

Homework Statement Solve for the volume above the xy-plane and below the paraboloid z=1-x2/a2-y2/b2 I have gotten an answer that is close to the correct one, but I can't figure out where I am wrong. Homework Equations Solution: Volume is = ab\pi/2 The Attempt at a Solution...

To find the probability of a particle being at position x we use <\Psi|\Psi> where the complex conjugate ensures that the answer is real. This means that we're looking at the square of the wave function to determine the probability of finding the particle. Now to determine the probability...

Homework Statement Find a transform T that maps the unit square in the u-v plane to a quadrilateral with corners (1,2), (3,3), (4,2) and (2,1) to the x-y plane. Homework Equations The Attempt at a Solution I've been able to create the proper region in the x-y plane when I have the transform...

Homework Statement Convert the Riemann's Sum to an integral: (1/50) * [(sqrt(1/50)) + (sqrt(2/50)) + (sqrt(3/50)) ... + (sqrt(50/50))] Homework Equations The Attempt at a Solution (1/50) times Integral (upper limit 1 and lower limit 0) of sqrt(x) dx Is my solution correct?

Homework Statement This is just something I've been wondering, but since derivatives have the formula: dy/dx = lim h-> 0 of (f(x+h) - f(x)/h) And that formula can prove a lot of derivatives. Does a similar formula exist that can prove integrals? Homework Equations The Attempt...

Homework Statement A voltage of 60cos(4 \pi t) V appears across the terminals of a 3mF (milli-farad) capacitor. (which is equal to .003 F [farad]). Calculate the current through the capacitor and the energy stored in it from t=0 to t=.125 s Homework Equations Current through an ideal...

Hi, I am currently in Calculus 2 at my local college and I am having trouble wrapping my head around Improper Integrals. The question below I have been working on for awhile and I think i have an answer but was wondering if anyone could confirm if I was thinking about this question the right...

This is probably an easy question, but my math is not good enough to answer it. For Gaussian integrals: \frac{\int \Pi_i [dx_i] x_k x_l e^{-\frac{x_i A_{ij} x_j}{2}}} {\int \Pi_i [dx_i] e^{-\frac{x_i A_{ij} x_j}{2}}}=A^{-1}_{kl} As far as I understand it, in QFT, Aij is a local operator. So...

Homework Statement prove that 2√2 <= ∫(from 0 to 1) (√x+8) dx <= 3 Homework Equations The Attempt at a Solution well...my only idea on how to solve this would be to evaluate the middle term, but my prof says it's not allowed. Do I just assign functions to the left and right...

Given two functions f_{1}(x) and f_{2}(x) that are differentiable on [a_{1},a_{2}] and \int^{a_2}_{a_1}f_1(x)f'_{2}(x)dx=b_2, how would one calculate \int^{a_2}_{a_1}f_1(x)f'_{2}(x)dx? This is not a homework problem. I saw it on the internet and realized that I did not know where to begin...

Hello! I have a hard time getting to know what this exponential W(J) really is about. What is it even called? Zee writes: Z(J) = Z(J=0) * e^(i W(J)), and I suppose that this is the term that should be evaluated by summing over all possible pair of sources? What is W(J) for a system with 2...

Homework Statement Compute the following line integral: \int_{\gamma} |z|^2 dz where \gamma(t) is the line segment from 2 to 3 + i Homework Equations Green's Theorem The Attempt at a Solution I originally started by saying that y = x - 2 and subing that into the equation "x^2 + y^2"...

Homework Statement Suppose 0<a<1. 1) Show that 0<Integral(0 to a)1/(sqrt(1-x^2)<=Integral(0 to a)1/(sqrt(1-x)<=2 2) Show that I(a)=Integral(0 to a)1/(sqrt(1-x^2) is increasing and bounded by 2. 3) Deduce that Integral(0 to 1)1/(sqrt(1-x^2) exists and has an improper integral...

The Questions Let y(x) be the position of a particle at time x. Suppose that we know that the velocity of a particle satisfies the differential equation: y'(t) = ty with y(0) = 1. We will try to give a reasonable method to approximate some of the positions of the particle. a.)...

Homework Statement My professor was explaining that he has a several thousand page, Russian book of integrals in his office for solving for practice. Has anyone ever heard of it, or even know the title of the book. I just want to be able to google search it and see how much it costs...

Hello, I have question about using Dirichlet's Convergence Test which states: 1. if f(x) is monotonic decreasing and \lim_{x\rightarrow \infty} f(x)=0 2. G(x)=\int_a^x g(t)dt is bounded. Then \int_a^\infty f(x)g(x)dx is convergent. But what about the following situation: f(x)=1/x g(x)=cosxsinx...

Hello fellow physicists! Last meeting with my supervisor I had just recovered from disease so all I have left are some equations for the math behind path integrals that don't make to much sense.. I was wondering if, maybe someone can help and clarify what he was trying to get at. It would be...

Homework Statement It's been a couple of years since I've done real math, so I'm kinda stuck on this one. This is actually part of a physics problem, not a math problem - but I'm stuck on the calculus part. I'm trying to solve this guy: \int \limits_{-\infty}^{\infty}...

Homework Statement what is the difference between path integral and line integral? Homework Equations n/a The Attempt at a Solution is path integral over a scalar function and line integral is over vector function? I'm confused about this pls help me understand thanks...

Homework Statement f(x,y,z) = g(√(x^2 + y^2 + z^2)) g(t) = t-5 evaluate ∯ f(x,y,z)ds where S is sphere x^2 + y^2 + z^2 = 9 Homework Equations The Attempt at a Solution i don't know how to go about it. can someone help me with this, how to approach this from start to end...

Homework Statement Using substitution, find the integral of 32x2/(2x+1)3 Homework Equations The Attempt at a Solution I initially tried plugging u in for 32x2 but that wouldn't work because it won't cancel out with the problem below it anyway. I'm pretty sure we are not expected...

Homework Statement A water tank is shaped like an inverted cone with height 6 m and base radius 1.5 m If the tank is full, how much work is required to pump the water to the level of the top of the tank and out of the tank? Homework Equations Integral of ( density * g...

[b]1. Determine whether the following diverges or converges. If converges, evaluate it. a) integral from 1 to infinity of: 1/(2x^2 + x) dx b) integral from 0 to 1 of: 1/(2x^2 + x) dx I just want to check my answers. I got a) diverges and b) converges with value of ln|3/2|. Do these answers...

Homework Statement Evaluate double integral (x-y)^2 (sin (x+y))^2 dxdy taken over a square with successive vertices (pi,0), (2pi,pi), (pi,2pi), (0,pi) Thank you.

Hey, I've been reading a bit in the QFT book by Pierre Ramond about loops and i stumbled about some derivations in appendix B that I can't follow. First Ramond derives a formula for integration of momenta in arbitrary dimensions \int \frac{d^Nl}{(l^2+2p\cdot...

Homework Statement If you jump out of an airplane and your parachute fails to open our downward velocity t seconds after jumping is approximated for g=9.8m/sec^2 and k=.2 sec, by v(t)=(g/k)(1-e^(-kt)) So, if you jump from 5000 meters above the ground write an equation whose solution...

Homework Statement a) Solve:^{Pi}_{0}\int\frac{sin(x)}{1 + cos²x}dx b) Proof that for each f, continuous in [0, a], ^{a}_{0}\int{f(x)}dx = ^{a}_{0}\int{f(a-x)}dx c) Use a and b to solve ^{Pi}_{0}\int\frac{x sin(x)}{1 + cos²x}dx Homework Equations / The Attempt at a Solution a) t =...

This is really a full on homework question but it WILL help me to solve my homework... by helping me fully understand the integral. So I am trying to understand exactly what the indefinte integral means? heres my train of thought... if our function F(x) = x2 then its derivative is F'(x)...

Since I'm trying to make sense of the application of a concept, I figured I'd post this thread here. If this belongs in the homework forum, I sincerely apologize. For the longest time I would do integral problems in Calculus. I figured I understood how to do them because after I finished...

Homework Statement Hi All, I've been having great difficulty making progress on this problem. Suppose gn converges to g a.e. on [0,1]. And, for all n, gn and h are integrable over [0,1]. And |gn|\leqh for all n. Define Gn(x)=\intgn(x) from 0 to x. Define G(x)=\intg(x) from 0 to x...

You can say an integral is the area under a curve and the derivative is the slope. What are the equivalents for line and surface integrals? I've tried google and wikipedia but I can't find a dumbed down version. :cry: I know that line integrals are related in some way to arc length since a line...

I couldn't decide whether to place this in the Physics or the Math section of the forums, deep down it is really a Math question for Physics problems. So mods please move if you feel it would be more appropriate in the Physics section. So when doing calculations, I always like to make sure my...

What is the relationship between the quantum mechanical path integral and classical mechanics path integral?

Homework Statement The area bounded by the curve y = f(x) = x4 -2x3 + x2 + 3, the x-axis and the ordinates corresponding to the minimum of the function f(x) is? The Attempt at a Solution I found out the critical points as x= 0,1,1/2 Out of these, the minima occurs at 0 and 1 Since...

In another forum, I have been challenged to prove mathematically that a certain idea which consists of fields of discrete elements will satisfy http://en.wikipedia.org/wiki/Divergence_theorem" . The fields are not expressible in terms of a differentiable function but rather consist of discrete...

This is a very basic question, but I just started wondering about it. First which is the original quantity and which is the derived one. I mean is the displacement by definition is integral from a to b v(t) dt or is it the distance from the starting point to the finishing point or change in...

Hi guys, i was just wondering if there is some book or whatever that has a list of loop integrals. More specifically, I am looking for one-loop integrals in the lightcone gauge with an arbitrary number of propagators. I found a paper by Leibbrandt which tells me how to calculate them, but I...

[PLAIN]http://img42.imageshack.us/img42/8669/20183046.jpg Need to show it is approx. equal to (1/3)!/x^(1/3) Any suggestion of further substitution? I need to change the limits.

Find all possible values of the integral (1+3z+5z^2)/z^n about the circle of radius 1 centered at 0. n is any integer. Please help.

Homework Statement Set up but do not evaluate a triple iterated integral to evaluate, \int \int \int_{V} dV where B is a region in R^{3} bounded by the planes, z=0, z=3x, x+z =4, y=0, y=2. Homework Equations The Attempt at a Solution I'm just curious to see if what I've...

Homework Statement Let f be continuous on the interval [0,inf] with abs(f(x)) < M, set F(u) = \int \frac{u*f(x)}{u^2 + x^2} integral from 0 to inf (bad with latex) prove that lim F(u) as u --> 0 = f(0)Homework Equations noneThe Attempt at a Solution I split the integral into the intervals...

Homework Statement I'm trying to solve a problem where you are asked to find the derivative of an integral where both limits of integrations contain variables Homework Equations Definition of integrals, derivatives The Attempt at a Solution For problems where you have an...

Homework Statement Prove that if \int_{-\infty}^{+\infty} f exists, then \lim_{N\rightarrow \infty of {\int_{-N}^{N} f} exists and is equal to the first equation. Show moreover, that \lim_{N\rightarrow \infty of {\int_{-N}^{N+1} f} and \lim_{N\rightarrow \infty of {\int_{-N^2}^{N} f}...

vollume bounded by x+y=4 y^2+4z^2=16 not sure how to set this up also I 6y+x dx + y+2x dy along (x-2)^2+(y-3)^2=4 also vollume bounded above by z=4-4(x^2+y^2)^2 below by (x^2+y^2)^2-1

What is the symbol of an integral with a circle in the middle called? I am asking because Gauss's Law is defined to be equal to that integral of the dot product of E and dA.

Homework Statement ∫ [-2pi,2pi] (x^2)(sin(e^x))^8 dx <= (16pi^3)/3 Homework Equations The Attempt at a Solution I know that the function is almost 0 when x<0 I'm just not sure how to show this mathematically

I am having much trouble with indefinite integrals - i get most of the basic theory behind them but as soon as i am confronted with a larger more complex question i get stuck too easily. These questions are not for my homework, they are just practice for my test. Any hints, tips and general...