Integrating Definition and 971 Threads

Hey, I've just been following this proof for a integrating factor of (xy), http://mathworld.wolfram.com/ExactFirst-OrderOrdinaryDifferentialEquation.html it starts at at equation (22) I understood it all a few days ago and now I seem to have forgotten this one step. It says...

1. The problem statement, Prove that for any n\inN and any real umber x, \sum\stackrel{n}{i=0}\left(\stackrel{n}{i}\right)\frac{x^{i+1}}{i+1}=\frac{1}{n+1}((1+x)^{n+1}-1) 2. I tried to integrate both sides of Bionomial Theorem However, I'm not sure what to do at the first place. :(

question: integral of [(3-ln2x)^3]/2x my workings: I let u = 3-ln2x then du= -2/x dx so -1/2du = 1/x dx this leaves me with -(1/2)*integral of u^3/2 du I take the bottom 2 out to get -(1/2)*(1/2) * integral of u^3 du which is -1/4 * (u^4)/4 then I sub u into get -1/4...

Homework Statement e∫^P(x) ∫\frac{x-2}{x(x-1)}dx The Attempt at a Solution so i split it into ∫\frac{x-2}{x(x-1)}dx = ∫\frac{2x-1}{x^2-x}dx - ∫\frac{x+1}{x^2-x}dx = ln(x2-x) - ∫\frac{x}{x^2-x} - ∫(x2-x)-1 = ln(x2-x) - ln(x-1) - ∫(x2-x)-1 ok. having problems working out...

I attached a file that shows the free EM action integral and how it can be rewritten. I would like to know how to go from the first line to the second. I have to integrate by parts somehow, and I know surface terms get thrown out, but I do not know how the indices of the gauge fields should be...

Homework Statement find ∫4cosx*sin^2 x.dx Homework Equations The Attempt at a Solution ∫4cos x * 1/2 (1 - cos2x) ∫2cosx - 4cos^2 x. Then i don't know whereto go from here??

Question: When determining the coefficients of the partial fractions for say 5 or more coefficients... Do you find it easiest to set up linear equations and solving? Any advice would be appreciated... Next question.. look in paint doc... why would I3 not be equal to I21??

I am really struggling with proving a ODE by means of using the integrating factor method. My original problem was a Laplace transform q'+2q=5sin(t) where q(0)=0 I believe i have got the correct naswer for this as being:- q= e^-2t +2sint-cost I just need to confirm this i have my...

Homework Statement (3(x^2)y + 2xy + y^3)dx + (x^2 + y^2)dy = 0 The Attempt at a Solution This is from my notes, so I already have the answer. I just don't understand the very last step with the integrations. (3(x^2)y + 2xy + y^3)dx + (x^2 + y^2)dy = 0 My = 3x^2 + 2x + 3y^2 Nx = 2x...

Homework Statement The picture attached shows an insulated board (12m x 4m) with uniform charge density σ. Integrate to find the electric field 8 cm above the center of the board.Homework Equations I found the equations \vec{E}=\int\frac{kdq}{r^{2}}\hat{r} and dq=σdy (both from google)The...

Hi all, I am doing some Laplace Transforms as part of my HND, i have got an answer for this question q' +2q = 5sint q(0)=0, t(0)=0 But i need to prove it by means of using an integrating factor method. My original answer is:- e^-2t +2sint-cost does this look right? I also have...

Homework Statement If you look at the answer you will see that they integrate sin43x into (sin53x)/5. well, if you can do that why not just integrate 3cos53xdx into (cos63xdx)/2? why go through all the trouble of dividing it into parts? it is true that (cos63xdx)/2 = 0 but i still don't...

Okay I'm working on making a ballistics calculator and I need to know how to integrate this. To get velocity, and ultimately to get time of flight. So that I can use that to determine drop with an angle of 0.

Homework Statement m' = G O^1/2 m^(-1/2) where m' = dm/dt. Find m by integrating this expression wrt to time (indefinite). Homework Equations We have G = m'/m and O = constant/G^2 and m is a function of time m(t) The Attempt at a Solution I know that integral of m'/m...

Identify one (1) lesson on circles that could integrate the Seed of Life in the delivery of the lesson. I need help on this urgently

Homework Statement Find the general solution of the given differential equation cosxy'+(sinx)y=1 The Attempt at a Solution I divided everything by cosx and got : y'+(tanx)y=secx then after doing e to the integral of tanx i got : ∫d/dx[secx*y]=∫secx after integrating and...

Hey guys, I have : df=c(x^2)(y^2)dx + (x^3)(y)dy along paths (0,0) to (1,1); and also paths (0,0) to (0,1) to (1,1) (where (x,y)) where c is some constant. I am having difficulty doing this particular integral, what type of integral is it and how do I go about solving it? Thanks!

alright guys, I've been trying to tackle this for a couple of hours now. dy/dt-2y=4-t my integrating factor is e^(-2t) of course. dy(e^(-2t))/dt-2ye^(-2t)=4e^(-2t)-te^(-2t) then I get completely lost. how do I integrate when it's like this? My book simplifies the above equation into...

Homework Statement Show: 0∫2∏ δ(sin θ - k) dθ equals θ(1-|k|) * 2/sqrt(1-k2) Homework Equations integrating dirac-delta function The Attempt at a Solution [sin (2pi) - k] - [sin 0 - k] ??

Integrating Factors for ODEs (Question from Boas) Find an integrating factor by inspection to make the below differential equation exact. (y^2-xy)dx+(x^2+xy)dy=0 I've been inspecting, but I'm not seeing it! Is there a way to analyze this in my head that will lead me more easily to the...

Homework Statement Integrate: \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-2\sqrt{x^2+y^2+z^2}}dxdydz hint: use spherical integration Homework Equations p=\sqrt{x^2+y^2+z^2} dV=dp d\phi p sin\phi p d\theta The Attempt at a Solution...

Homework Statement Solve the integral annd express it through the gamma f Homework Equations cos(theta)^(2k+1) The Attempt at a Solution

Problems integrating in a "for" loop in Matlab My problem strikes me as embarrassingly simple, so hopefully someone can set me straight with ease. I'm writing a Matlab code in which I'll be wanting to do a good amount of integrating of products of various eigenfunctions. Presently, I'm just...

Problems integrating in a "for" loop in Matlab My problem strikes me as embarrassingly simple, so hopefully someone can set me straight with ease. I'm writing a Matlab code in which I'll be wanting to do a good amount of integrating of products of various eigenfunctions. Presently, I'm just...

Homework Statement \int_0^{\infty} \ln \left( \frac{e^x+1}{e^x-1} \right) \mbox{d}x \int_0^{\infty} \frac{1}{x^n+1}\ \mbox{d}x\ \forall n >1 Homework Equations - The Attempt at a Solution I've tried IBP and separating the ln into two terms and failed. I've also tried a...

Homework Statement \int \frac{1}{2t^2+4} \mathrm{d}t[\tex]Homework Equations \int \frac{1}{Z^2+A^2} \mathrm{d}Z = \frac{1}{A} \arctan{(\frac{Z}{A})} + cThe Attempt at a Solution Looks quite easy, but this is what's annoying me: the two methods below should be identical, but something's gone...

My question is taking the Bethe-Bloch equation and integrating to find the range of an energetic Deuteron. I first have the Bethe-Bloch equation, \frac{dE}{dx} = -\rho 0.1535 \frac{Z_{p}^{2}}{\beta^{2}} \left(\frac{Z_{A}}{A}\right) \left[ln\left(\frac{2 M_{e} c^{2} \beta^{2}}{IE\left(1 -...

Homework Statement If (the integral from -3 to 2)f(x)dx=-1, (the integral from -1 to 5)f(x)dx=8, and (the integral from -3 to 5) f(x)dx=6, then (the integral from -1 to 2)f(x)dx= ? Homework Equations This is the part I'm struggling with. The Attempt at a Solution I...

I've got a Mathematica question which might be quite basic, but I couldn't find much about it in the documentation (possibly because it's so basic) so please bear with me! I have a set of data, call it xi(ρ), which I want to integrate over some distribution function (log-normal in this case)...

I keep struggling to find a solution to this IVP. We are supposed to use integrating factors y'-(1/t)y=8t^2+te^t t>0, y(1)=6 I get an integrating factor of (1/t) and general solution of y=4t^3+te^t+c but then i get e+2 for c. This doesn't seem correct to me, any suggestions?

In my differential equations class I have been given a problem which involves solving dx/dt=u where u=u(x) I know that this is done by separation such that ∫dx/u = ∫dt, and then the constant of integration found using initial conditions, however I am getting myself all worked up and confused as...

Homework Statement ∫r^3/(4+r^2)^(1/2) dr Homework Equations ∫udv=uv-∫vdu The Attempt at a Solution I know that integration by parts must be used. I tried doing it with 4+r^2 as u, but kept running into issues..then I got an answer but it appears to be wrong. I guess I am not sure...

Homework Statement I'm having some trouble trying to integrate the following function Homework Equations \int([x/(logx)]dx) The Attempt at a Solution I have tried integration by parts but I get stuck with harder integrals. What I'd like to know is that this function could be...

I hope I am posting this in the correct area. This is not specificly a homework question, but something that keeps stumping me on numerous Electrostatic problems. When attempting to Intigrate for finding the electric field or potential, I frequently end up with an integral over the form ∫∫∫...

Homework Statement Hi, I submitted this question on here the other day a user suggested some topics which might help so I have went away and tried this and this is what I have came up with. I just want to know what I have so far is right also I need help with integrating the rhs of the...

This is the ODE: y' + siny + xcosy + x = 0. The problem is: Find an integrating factor for the ODE above. You can see my solution to the ODE here: https://www.physicsforums.com/showthread.php?t=543662. from my solution it seems that e^x(sec^2(y/2)) must be an integrating factor. but I fail...

Hello, I am trying for a couple of hours now to integrate these equations ( http://en.wikipedia.org/wiki/Euler%27s_equations_%28rigid_body_dynamics%29 ) with the Euler's method: \dot{f}=\partial{f}/\partial{t}\cong\Deltaf/\Deltat=(f(t+\Deltat)-f(t))/\Deltat . I am trying to do this...

I'm taking a probability class where multivariate calculus was not a prerequisite, but some of it is coming up, I get the concept of, say integrating over a region, but get lost in some of the mechanics Here is the problem (I don't want a full solution): A point is uniformly distributed...

Homework Statement Integrate the following: (sin(x)/x)^4 between negative infinity and infinity. Homework Equations The residue theorem, contour integral techniques. The answer should be 2pi/3 The Attempt at a Solution I'm not even sure where to start honestly. I define a function...

Homework Statement Find an integrating factor for: xdy - (y + x^2 + 9y^2)dx = 0 Homework Equations P(x,y)dx + Q(x,y)dy = 0 Δμ = μyP - μxQ. where μ is the integrating factor. The Attempt at a Solution well, I don't know what I should do. I can use the formula I wrote but that would...

Homework Statement the definite integral of (x-1)/(x^3+4x^2+3x) from x=1 to x=3 using partial fraction decomposition. I know the answer should be (5/3)ln2 - ln3. Homework Equations The Attempt at a Solution After integrating, I got -(1/3)ln(3x) - (2/3)ln(x+3) + ln(x+1) . The...

Homework Statement Integrate the function, f(x) = √(12 -x2) Homework Equations n/a The Attempt at a Solution I tried splitting the function up as follows: f(x) = √(12+x)*√(12-x) then I tried substituting in, w=12-x and dw=-dx, to get...

Homework Statement There is a current of 20 A in a resistor that is connected in series with a parallel-plate capacitor. The plates of the capacitor have an area of 0.80 m2, and no dielectric exists between the plates. Find the value of the line integral B ∙ dl , where the integration path C...

Homework Statement The problem could be any variation of dx/(x2-2x) Homework Equations ∫dx/x2-a2 = 1/2a ln ((x-a)/(x+a)) + C The Attempt at a Solution I understand the answer to be 1/2 ln ((x-2)/x) + C My question is why is it just x on the bottom in the solution? Shouldnt it...

I'm having a problem with NDSolve. See attached picture. I have a package generating a set of ODE's, which I display, and then the next line is the NDSolve integration. I get an "Encountered non-numerical value for a derivative at t==0" error, and I can't spot the mistake. The one thing that...

1. Relevant problem integrate from 0 to infinity of r^2exp^(-r/a0)dr Homework Equations I'm also given; integral from 0 to infinity of x^nexp^-x dx = n! The Attempt at a Solution I'm just wondering if I can split up the exponential to make it look like this form. Eg; integrate from 0 to...

I have a data curve with discrete time points that I imported into MATLAB. The x-axis is an array named t: t = 1.0e+003 * 0.0319 0.0505 0.0851 0.1037 0.1356 0.1648 0.2021 0.2313 0.3616 0.5823 0.8880 1.1778 1.4996...

Homework Statement For t < 0, an object of mass m experiences no force and moves in the positive x direction with a constant speed vi. Beginning at t = 0, when the object passes position x = 0, it experiences a net resistive force proportional to the square of its speed: Fnet = −mkv2, where...

Homework Statement The question is what has gone wrong in this proof, it is worth noting this a definite integral between pi/6 and pi/4: ∫ tan(x) dx = ∫ sin(x)/cos(x) dx Let u = 1/cos(x) and dv = sin(x) dx So du= sec(x)tan(x) and v = -cos(x) When we substitute back in we get: ∫ tan(x)...

Homework Statement How do I integrate \int_0^1 xJ_0(ax)J_0(bx)dx where J_0 is the zeroth order Bessel function?Homework Equations See above. Also, the zeroth order Bessel equation is (xy')'+xy=0The Attempt at a Solution Surely we must use the fact that J_0 is a Bessel function, since we can't...