Integrating Definition and 940 Threads

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...

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...

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...

Homework Statement I need to find the integral of the following equation.. integral from 0 to 8 of {(2H[x-0]+2H[x-4])*(x/8)}dx The Attempt at a Solution Im am not sure what the integral of the heaviside function is? is it 1 or 0? Any help would be appreciated! Thanks

If u(x,y) and v(x,y) are two integrating factors of a diff eqn M(x,y)dx + N(x,y)dy, u/v is not a constant, then u(x,y) = cv(x,y) is a solution to the differential eqn, for every constant c.

Find the length of the curve: r(t) = <2t, t2, (1/3)t3> r'(t) = <2, 2t, t2> From bounds of t: 0 to 1. So length = integral of the modulus of r'(t): Integral of sqrt(t4+4t2+4) I'm just dead stuck on how to attack it. I tried to make it integral of sqrt((t2+2)2), and then just...

Hello I have problem with integrate \int_{0}^{\frac{\pi}{2}}d\phi_1...\int_{0}^{\frac{\pi}{2}}d\phi_{n-2}sin^{2(n-1)}\phi_1...sin^{2(n-k)}\phi_k ...sin^4\phi_{n-2} Please help me.

Homework Statement Integrate exp[abs(x)+3]*delta(x-2) dx, -1, 1 2. The attempt at a solution f(x)=exp[abs(x)+3]*delta(x-2) f(2)=148.4 Integrate exp[abs(x)+3]*delta(x-2) dx, -1, 1 = 0 [b]3. Why is the answer 0?

Hi, this is not really a homework problem, but something that came up during my research, upon trying to integrate some empirical function. This function consists of many terms, but specifically, there is a term containing double exponential functions which is giving me some trouble. If...

There are 3 equations 1/ Continuity equation Av=constant 2/ Bernoulli's equations P+1/2*p*V^2+pgy=constant 3/ Poiseiulle's equation Question1: If a single blood vessle is narrowed by the build-up of plaque so that its inner radius is reduced. How can I use above three...

My book stated the following theorem: If the functions P(x) and Q(x) are continuous on the open interval I containing the point x0, then the initial value problem dy/dx + P(x)y = Q(x), y(x0)=y0 has a unique solution y(x) on I, given by the formula y=1/I(x)\intI(x)Q(x)dx where I(x) is the...

Hi, Say I have an acceleration vector in polar coordinates: a = -30e_r where the unit vector e_r points in the same direction as the Cartesian unit vector j. How can I integrate that vector so that I have the velocity vector in polar coordinates? I know that if I have an acceleration vector...

Homework Statement \int\frac{4x^5-1}{(x^5+x+1)^2}dx Homework Equations This is in the section on Partial Fractions. The main idea in this section was that you get the integral down to a sum integrals of the following forms: \int\frac{dx}{(x+a)^n} , \int \frac{x dx}{(x^2 + bx + c)^m} ...

Please Help! Integration! Hi! I'm having a little problem with an exercise and I don't know how to sort it out. Basically what I have is a tube of 5mm ejecting spray fuels. At the exit plane I have positioned lasers to measure the volume flux at different locations, starting from one side...

Homework Statement How would you find the integral of y''/y (with respect to x)? Homework Equations The Attempt at a Solution I have absolutely no idea how to begin. All I know is that if it were y'/y, it would be log(y) + c. Perhaps the integral here has something to do with...