Integrating Definition and 940 Threads

Homework Statement The context of this question is physics related but the problem I am having is purely mathematical. g(t)= e^(-(a^2)(t^2))*e^(iwt) (a and w are just constants, i is sqrt(-1), not a constant) I need to integrate this function with respect to t from -infinity to...

Hi Everybody, So basically I spent the summer working on some optics related stuff and now they want me to present my research work. This means I'm going to have to do numerical simulations for diffraction of Laguerre-Gaussian beam modes. In a word, the integrals are ridiculously long and...

Homework Statement Use the method of trigonometric substitution to evaluate the following: [SIZE="3"]\int\frac{x^{2}}{\sqrt{4-9x^{2}}} Homework Equations The only relevant equation that I could think of for this one was the trig identity: [SIZE="3"]sin^{2}\vartheta +...

The integral of a complex exponential ( e^(ix) ) over x from 0 to infinity is supposedly such that the value of the definite integral at the upper limit is zero and so it's just -1/i. Why is this? It's just an oscillating function after all.

Would anyone be able to help me do this? I have tried by parts, but did not make progress. As n gets large, the area gets smaller. Your help is appreciated. Z

Homework Statement Hi there. I was trying to solve this problem, from the book. The problem statement says: Integrate \nabla \times{F},F=(3y,-xz,-yz^2) over the portion of the surface 2z=x^2+y^2 under the plane z=2, directly and using Stokes theorem. So I started solving the integral...

Homework Statement This is from Peskin & Schroeder p. 14 in case anybody's interested. The function is U(t)=\frac{1}{(2\pi)^3}\int d^3p\, e^{-it \sqrt{p^2+m^2}}e^{i\vec p\cdot(\vec x-\vec x_0)} Homework Equations The Attempt at a Solution Essentially you write out the dot product as p\cdot...

While it's pretty easy to derive the infinitesimal version of the special conformal transformation of the coordinates: x'^{\mu}=x^{\mu}+c_{\nu}(x^{\mu} x^{\nu}-g^{\mu \nu} x^2) with c infinitesimal, how does one integrate it to obtain the finite version transformation...

Hi, guys. For an E&M/quantum mechanics problem I have to integrate the series below: Homework Statement Integrate \int{r^{2}e^{y r} \, dr}.2. The attempt at a solution Using integration by parts and and "differentiating under the integral" give the same answer: I= \frac{2...

Link: http://imageshack.us/photo/my-images/39/18463212.jpg/ This is a very long problem so I drew it to make things simpler. Part a) tells me to set up a double integral in polar coordinates giving the total population of the city. I have the following: 2π...4 ∫...∫ δ(r, θ) r dr...

Homework Statement indefinite integral: dx/(x*sqrt(9+16x^2)) Homework Equations Trig. Substitutions or parts?? The Attempt at a Solution I tried using integration by parts but its got pretty messy...it also resembles a tan trig substitution, but it's within a square root. I'm...

Homework Statement f(x, y, z) = x^2 ; G is tetrahedron bounded by the coordinate planes and the plane octant with equation x + y + z = 1 ∫ ∫ ∫ x^2 dzdydx I try to set up the ranges for x, y and z.. x+y+z = 1 z = 1-x-y...set the limits for z from z=0 to z = 1-x-y x+y+z = 1 if, z = 0, y =...

Homework Statement i have an equation that i want to solve for b: \int _0^1 (a+b x)^2 x^c dx=2 Homework Equations \int _0^1 (a+b x)^2 x^c dx=2 given: c>0 The Attempt at a Solution To evaluate the integral on the left hand side, I expanded the bracket as: (a+b...

I am having trouble with the below: [ 4* (x^3/y^2) + (3/y)] dx + [3*(x/y^2) +4y]dy=0 I found My= -8x^3y^-3 - 3y^-2 and Nx= 3y^-2 i then subtracted Nx from My and divided by [3*(x/y^2) +4y] [-8x^3y^-3 - 6y^-2] / [3*(x/y^2) +4y]. can you guys give me a hint as to where my error is?

Hi, I have a general question regarding the integrating factor of first-oder linear DEs. All textbooks that I've seen (which aren't too many) simply drop the absolute symbol when the factor has the form exp(ln(abs(x))). This would evaluate to abs(x), yet the books use simply x. Why is that...

Homework Statement consider the integral, {C_\ell } = \frac{{2\ell + 1}}{{2{j_\ell }(kr)}}\frac{1}{{{2^\ell }\ell !}}\int_{ - 1}^{ + 1} {\frac{{{d^\ell }({{({x^2} - 1)}^\ell })}}{{d{x^\ell }}}{e^{{\bf{i}}krx}}dx} how do you do it? Homework Equations l = integer, as in the...

Homework Statement My book shows that http://img845.imageshack.us/img845/4875/unleduot.jpg and then they arrived at the results [PLAIN][PLAIN]http://img202.imageshack.us/img202/5442/unleddq.jpg So my problem is that, how exactly did they drop the mu in the first picture?

Homework Statement Find the general function f(x,y) that satisifes the following first-order partial differential equations \frac{df}{dx}=4x^3 - 4xy^2 + cos(x) \frac{df}{dy}=-4yx^2 + 4y^3 The Attempt at a Solution I integrated both to get: x^4 - 2x^2y^2 + sin(x) + c(y) and -2y^2x^2 + y^4...

Homework Statement http://s39.photobucket.com/albums/e178/dorlomin/enviroment/?action=view&current=core2.jpg http://s39.photobucket.com/albums/e178/dorlomin/enviroment/?action=view&current=core2.jpg" Homework Equations In the question shown the equation is required to be integrated to...

Homework Statement ζζs yz ds S is the part of the plane x+y+z=1 that lies in the first OctantHomework Equations ζζs f(x,y,z) dS = ζζd f(x,y,g(x,y)) sqrt(1+(df/dx)²+(df/dy)²) dAThe Attempt at a Solution turned dS into dA, and attempted many different regions. Always got an area that was 4-6...

My lecturer told me that it's best not to integrate when you're a new student to kinematics because it's important to understand the principles of operation-- which is why we're not using it. On the other hand, I keep being told by this forum that calculus is the true way to fathom mechanics...

when integrating by trig substitution why do you use what you use?? for example int. (1+x^2)^0.5 dx why do you use x= tan u i mean obviously because it works, but if you didn't know it works how would you figure it out? i would think that you should use x=sinh u but I've been trying...

I came across this problem + solution: http://imageshack.us/m/715/2962/inteyk.png but I don't understand the calculus there. How can you integrate the stuff inside the brackets but not integrate that fraction?

I went through several threads about the integral of e^x^2 but I could not find anything about the proof why e^x^2 cannot be integrated as an elementry function. Could you explain why?

I need some help. I don't know how to make the intgral symbol, but here's the question. If somebody can get it started it'd be awesome. 1to e^10 1to e^6 1to e^2 1/xyz dxdydz

Homework Statement http://img857.imageshack.us/i/no34.jpg/ Homework Equations The Fundamental Theorem of Calculus, i.e., taking the derivative of an integral yields the original function. The Attempt at a Solution I am not sure how to go about integrating this function because I...

Hi all. My first time posting. Hopefully it will go well. :) For my ME Lab 1 class I need to numerically differentiate LVDT data to find acceleration of an damped-oscillating mass system and I need to numerically integrate accelerometer data to find displacement of the same...

Homework Statement Let f be a vector function, f = (xz, 0, 0), and C a contour formed by the boundary of the surface S S : x^2 + y^2 + z^2 = R^2 , x ≥ 0, y ≥ 0, z ≥ 0 , and oriented counterclockwise (as seen from the origin). Evaluate the integral (Closed integral sign) f · dr , directly as...

Homework Statement "Show that each of the given differential equations of the form M(x,y)dx + N(x,y)dy = 0 are exact, and then find their general solution using integrating factors μ(x) = e∫h(x)dx and μ(x) = e∫g(y)dy Homework Equations (x2 + y2 + x)dx + (xy)dy = 0The Attempt at a Solution...

Homework Statement Integrate (2rx-x2)1/2 with respect to x where r is a constant. Homework Equations The Attempt at a Solution Thanks

Suppose the dielectric material is fixed in position and filling the capacitor, and you would have this term in the way of calculating something. \int\nabla\cdot\left[\left(\Delta{D}\right){V}\right]{d}\tau where D is the dielectric displacement Now that turns into (by divergence...

If we have a definite integral given by f(x) = ∫sintdt with limits from 0 to x, can we integrate the function directly by substituting t as x because the variable involved in the integrand is a dummy variable?

Homework Statement This is part of a vibrating circular membrane problem, so if I need to post more details please let me know. Everything is pretty straight forward with the information I'll provide but you never know. We haven't really learned what these are, just that they are complicated...

If f is a smooth function defined on the plane then the integral of its gradient over any closed curve is zero. What about the integral of the 90 degree rotation of the gradient? In symbols, if grad f = (df/dx , df/dy) its 90 degree rotation is (-df/dy , df/dx)

\int^{1}_{0}\int^{0}_{-x} \frac{ysin(pi*y^2)}{1+y} dydx Not exactly sue how to start this. I know that I need to integrate with respect to y first then use that solution and integrate again with respect to x however I do not believe integrating the initial problem is possible. Is there another...

Homework Statement So I thought of an interesting problem, and here it is: Solve \int \frac{1}{f'(x)} df(x) = g(x) for f(x). Now, I checked Wolfram-Alpha to see if an answer existed, and they gave me this: f(x) = c_1 e^{\int \frac{1}{g(\xi)} d\xi} But, you know that Wolfram-Alpha doesn't...

Homework Statement (2x+y^2) dx +4xy dy=0,y(1)=1 Homework Equations The Attempt at a Solution I'm having trouble finding the correct integrating factor, been playing with it for an hour and have made NO progress so need help. \delta P/\delta y=2y \delta Q/\delta x=4y...

I will denote vectors in bold. Homework Statement Show that the curve C given by r=a*Cos(t)Sin(t)i+a*Sin2(t)j+a*Cos(t)k ( 0=<t=<pi/2 ) lies on a sphere centred at the origin. Find \int zdS under C *edit* There is a huge gap here and the equation has dissapered for me. But...

Homework Statement Given \int_{0}^{k\pi} cos^{2m}(\theta) d\theta = A Express \int_{0}^{k\pi} cos^{2m}(\theta) cos(2\theta) in terms of A. Totally Stucked .. :XI've substituted cos^{2}\theta = \frac{1+cos(2\theta)}{2} Then i get 1/2 A + another chunck of integral. I've used...

Homework Statement Integrate sin5(x/3)dx on the interval [0,pi] Homework Equations sin2(x)=1-cos2(x) dcos(x)dx=-sin(x) The Attempt at a Solution I split off one of the sins and then set my integral equal to (sin2(x/3))2*sin(x/3) switching in 1-cos2(x/3) afterward. Then I set u =...

I was looking at how to derive an integrating factor for a non-exact DE that has multiple variable dependency, i.e. µ is xy-dependent, and I found the explanation at the link in the middle of the page at equation (22) (link...

Homework Statement Solve with u-substitution ∫ (x-5)/√(x-6) dx Homework Equations The Attempt at a Solution This is what I have done so far and it doesn't seem to work out. I have a feeling I'm missing something. Any help would be appreciated. u=x-6 du=dx x=u+6 ∫...

Consider I(c)= \int_0^\infty \frac{x^{1-\epsilon}}{x+c} dx For what values of \epsilon are these integrals convergent? Would it be \epsilon \geq 0? Then I'm asked to use x^{-\lambda} \Gamma(\lambda) = \int_0^\infty d \alpha \alpha^{\lambda-1}e^{-\alpha x} for x>0 and the identity...

Homework Statement The problem says to compute the following integral. \int_{C}F\cdot dr Where F=<e^y,xe^y,(z+1)e^z> \ \ and \ \ r=<t,t^2,t^3>,0\leq t \leq 1 2. The attempt at a solution Basically when I plug everything in, I get an integral that CANT be solved. At first I thought to...

Homework Statement Context is cosmology but not really relevant to the integration. I've managed to integrate it using substitution but it didn't seem that neat. Coming back after two-years off and I'm a bit rusty at spotting the best substitutions (wasn't great to start with :))...

Hi everyone I am looking at integrating this function, \frac{dv}{dt}=g-\frac{c}{m}v So far i have rearranged the function to get, (\int1/g - \int1/(cv/m))* dv= \intdt Thanks JB

Homework Statement Integrate dy/dx=2y+4x+10 The Attempt at a Solution dy/dx-2y=4x+10 Integrating factor = e^(-2)dx=e^-2x multiply both sides by IF. (e^-2x)dy/dx-2y(e^-2x)=(e^-2x)(4x+10) dy/dx(e^-2x y)=(e^-2x)(4x+10) i don't know what to do next.

I'm learning integration by parts, and thought this would be a good test of my understanding. I've separated it into something that seems better. \int \frac{1}{x^2+x}dx = \int \frac{1}{x} \frac{1}{x+1}dx I'm guessing I use integration by parts from here, but which should I make u?

Homework Statement Sorry asking similar quesion again about absolute value. You can read the attachment. u(x) is the integrating factor. Why absolute value is omitted in the integration? and why the integrating factor is not "1/|x|", with the absolute sign Homework Equations The...

Homework Statement Well hello! :smile: I am still uncomfortable with partials. In my (fluid mechanics) text we introduce this "stream function" \Psi(x,y) such that u =\partial{\Psi}/\partial{y} and v =-\partial{\Psi}/\partial{x} where u and v are the horizontal and vertical components of the...