Integrating Definition and 971 Threads

Function is (x - 2xy + e^y) dx + (y - x^2 + xe^y) dy = 0 Okay so it is the standard convenient exact equation for newbies. Now here is the part that confuses me. (a) Let P(x,y) = (x - 2xy + e^y) dx & Q(x,y) = (y - x^2 + xe^y) dy The function is defined for all real Numbers on an x,y plane...

This is a problem that came to me when i was doing implicit differentiation and i got curious as to how to integrate a problem like this. I was fascinated by the simplicity if an equation would have a complex integration problem. Homework Statement ∫x^x(ln x + 1)dx, Question 1 ∫x^x dx...

Can someone tell me what the benefit of this is, and why it's been traditionally very hard? I've heard that many RF applications now do an S-i-P integration of an inductor, possibly for spatial and cost reasons.. What would be some considerations, though (i.e. does the inductor add any noise...

In an exercise with included solution I can't understand how integrating sin^2(ωt) gives T(period)/2 \intsin^2(ωt)dt = Period/2 I posted the whole problem below, because I had more doubts, but understood them typing up the problem. I appreciate any help. YOU CAN SKIP THE...

I looked online and it gave a really simple method to solve it and it ended up with the solution x-2tan(x) I took a really weird approach and I'm not sure if my answer is right, and I'm hoping if someone could take the same approach and confirm if I did it correctly. I basically separated the...

Guys, I read that integrating the ds gives the arc length along the curved manifold. So in this case, I have a unit sphere and its metric is ds^2=dθ^2+sin(θ)^2*dψ^2. So how to integrate it? What is the solution for S? Note, it also is known as ds^2=dΩ^2 Thanks!

Hey everyone, I had a recent post similar to this one, and everyone may have not understood it because I didn't use LaTeX, so here it is. Homework Statement Integrate the area under \frac{x}{3x} and above \frac{x}{3x^.5} between x=1 and x=4. Same as: \int \frac{x}{3x} - \frac{x}{3x^.5}...

Homework Statement \int \frac{dx}{(1+4x^2)^{3/2}} The Attempt at a Solution \int \frac{dx}{(1+4x^2)^{3/2}} Let x = \frac{1}{4}tan(u), dx = \frac{1}{4}sec^2(u)du \frac{1}{4}\int{\frac{sec^2(u)du}{(sec^2(u))^{3/2}}} \frac{1}{4}\int{\frac{1}{sec(u)}}du \frac{1}{4}\int{cos(u)}du...

In many problems I am asked to compute a vector integral: Consider for instance the following example: Two spheres with total charge +Q and -Q spread uniformly over their surfaces are placed on the z-axis at z=d/2 and z=-d/2 respectively. What are their total dipole moment with respect to the...

Homework Statement integrate x^0.5/(1+x^2) by using complex integration Homework Equations residue theorem The Attempt at a Solution my attempt at a solution is attached.i need help in finding where am i mistaken. thank's Hedi

Homework Statement Let U be the open set in R^2 consisting of all x with (Euclidean norm) ||x|| < 1. Let f(x,y) = 1/(x^2 + y^2) for (x,y) \not = 0. Determine whether f is integrable over R^2 - \overline{U}; if so, evaluate it. Homework Equations g:R^2 \rightarrow R^2 is the polar...

The reason I ask the aforementioned question is because I came across the expectation values of operators in Quantum Mechanics. And part of the computation involves integrating a function of the complex conjugate of x with respect to dx. So as an example let's say I have: ∫ sin (x*) dx where...

xdy-ydx=(x2+y2)2(xdx+ydy) (Hint: consider d(x2+y2)2)Homework Equations d(x2+y2)2 d(arctan(y/x))=xy|-y/(x2+y2)The Attempt at a Solution The answer is arctan(y/x)-(.25(x2+y2)2)=C I correctly solved other problems of this type, but this is the hardest one in the problem set and I have no idea how...

Hi guys! I thought it was intergrationintegration, i think its differentiation. Im having problems trying to figure out where to start with this question: A rectangular tank with a square base x meters and height h meters is to be made from two different materials. Material for the...

So, as you can see in the attached pictures, I needed to find the common area bound by the 2 curves. Is the method I have outlined correct because according to the marking scheme it just says \int g(x) - \int f(x) (The limits are the same, -3/2 to 1) The way I see it, this does not account...

Hello, I came across a problem the other day where the person integrated thrust force from 0 to y in respect to y. And that got me thinking: you integrate jerk to get acceleration and integrate acceleration to get velocity, so what do you get when you integrate a force, namely thrust force...

I have the function: f(x,y)= x*(y^2)*e^-((x^2+y^2)/4), with x and y from -3 to 3 I took the integral of this function and got 0 as my answer. I need to find the average value, which is 1/area multiplied by the double integral. Since the double integral is 0, would the average value also be...

Homework Statement Hello, I'm new here and it seems that this place would be the right place to post, well, I'm just starting up with Integral Calculus, and I think I'm stucked up with integrating fractions like this one. Integral of 3/t^4 dt from 1 to 2 [b]2. Homework Equations yeah...

Converting to Spherical Coordinates...then integrating? Am I doing this right? Homework Statement Consider the integral ∫∫∫(x2z + y2z + z3) dz dy dx, where the left-most integral is from -2 to 2, the second -√(4-x2) to √(4-x2) and the right-most integral is from 2-√(4-x2-y2) to...

Homework Statement integrating x^3lnxdxHomework Equations The Attempt at a Solution i let u = lnx du/dx = 1/x xdu = dx x=e^u substituting that, i got e^(4u)udu then i let v = 4u dv/du = 4 1/4du = dv substituting that, i got 1/4integral e^v vdv I haven't gone beyond that step yet. I was...

I would like to take a physics example:- Suppose force is acting and is a function of distance x from origin. So F = kx Generally when we have to find the force on a say, a stick then we say - let's suppose a small element dx and then small force dF on this element is kdx I don't...

Hi, I have a question about integrating over the phase of a function in Mathematica. The origins of this problem is in scale analysis. f(x,t)= \sum_n a_n \cos (n(kx-\omega t)) for k,\omega \in \mathbb{R}. I want to integrate an expression dependent on f over the phase \theta_n =...

Hi, I need to find ∫ln(x+1)/(x^2+1)dx I think it might involve recursive integration by parts, so first I set: u=ln(x+1) dv = 1/(x^2+1)dx du=1/(x+1)dx v=ArcTan(x) ∫ln(x+1)/(x^2+1)dx = ArcTan(x)Ln(x+1) - ∫ArcTan(x)/(x+1)dx Then I integrated by parts again, so...

Hi there, I am trying to integrate this: http://imm.io/oqKi I should get the second line from the integral, but I can't show it. This should somehow relate to the Heaviside step function, or I am completely wrong. Any ideas? Sorry about the url, I fixed it.

Hi everyone. I am trying to integrate the following: \int^{\frac{π}{2}}_{-\frac{π}{2}}\int^{acosθ}_{0}\int^{\sqrt{a^{2}-r^{2}}}_{-\sqrt{a^{2}-r^{2}}}rdzdrdθ Here's my work: =2\int^{\frac{π}{2}}_{-\frac{π}{2}}\int^{acosθ}_{0}r\sqrt{a^{2}-r^{2}}drdθ I use substitution with u=a2-r2 to...

Hi, I am having difficulty understanding the following: \int^{2π}_{0}(x+y)\,dθ = \int^{2π}_{0} 2a\,dθ = \textbf{4}πa where x and y are the generator lines of an elipse, a is the semimajor axis and θ is the angle formed by x and the major axis. I understand that x+y = 2a. However I...

Homework Statement ∫y=e^(-2x^2)dxHomework Equations The Attempt at a Solution I can't recall any method for this. I know that the integral of e^x is e^x, but I know that in this case the integral would not be the same as the original function because the derivative of -2x^2 would be -4x. Can...

Having a bit of trouble with this equation, I need to find V explicitly and this would obviously be done by factorising and integrating, but I can't seem to factorise it correctly. I have what I think is the correct answer but can't do the steps to get there. Any help would be greatly...

Hi I am trying to integrate Newtons equations for my system a = \frac{F}{m} = \frac{d^2x}{dt^2} This is only for the first coordinate of the particle. I wish to do it for y and z as well, but let us just work with x for now to make it simple. The force in the x-direction depends on...

I can't figure how to solve this problem. Is says ∫∫(x^2)y dA where R is the region bounded by curves y=(x^2)+x and y=(x^2)-x and y=2. I can't figure how to do the limits with that. Please help!

Heres the differential rate equation for a 0 order reaction in chemistry: Rate = {{-d[A]} / {dt}} = k which can be rearranged to this: -d[A] = dt k and when you integrate this you get the integrated rate equation but I don't understand how this works. The site I'm reading says you integrate...

Homework Statement integrate:13((4^x)+(3^x))dx Homework Equations The Attempt at a Solution I know the solution is 13((4^x)/ln(4) + (3^x)/ln(3)) + C Can someone explain to me how this works? I don't know where the ln's are coming from. How would I differentiate this back to...

Homework Statement I need to understand how to integrate \int_{0}^{t}\int_{0}^{s} \delta(\tau-\tau')d\tau d\tau' The solution is min(t,s) Homework Equations See aboveThe Attempt at a Solution min(t,s)

Hello. I am having trouble conceptualizing and/or decisively arriving to a conclusion to this question. When finding the area enclosed by a closed polar curve, can't you just integrate over the period over the function, for example: 3 cos (3θ), you would integrate from 0 to 2pi/3? It intuitively...

Homework Statement Suppose that the force acting on a particle is factorable into the following forms. (a) F (x,t) = f(x)g(t) (b) F (v, t) = f(v)g(t) (c) F (x, v) = f(x) g(v) For which of these cases are the equations of motion integrable Homework Equations F = md2x / dt2...

So I just learned about these integrating factors and their utility in solving first order linear differential equations today. My mind is just kind of blown how it ends up simplifying the integration so much. Thats really pretty much the main thing I wanted to say... lol. But also, how the...

Homework Statement I have this statement: If M(x,y)dx+N(x,y)dy=0 is a homogeneous DE, then μ(x,y)=\frac{1}{xM+yN} is its integrating factor. The problem is, how do we derive this integrating factor? Homework Equations For homogeneous DE, we have f(kx,ky)=k^n*f(x,y) We also have...

Homework Statement There's a step I don't really understand in some "proof". d \left ( \frac{\mu }{T} \right )=-\frac{3R du}{2u}-\frac{Rdv}{v}. Now he integrates both sides to get \frac{\mu}{T}- \left ( \frac{\mu}{T} \right ) _0=-\frac{3R}{2} \ln \frac{u}{u_0}-R \ln \frac{v}{v_0}. I don't...

Homework Statement Solve the differential equation: t^2 y' + y^2 = 0 The Attempt at a Solution Now, it's definitely possible to solve this via separable of variables. But I am curious to know if I can solve it with an integrating factor. Having done some reading, I noticed that this...

I am not understanding integration with polar coordinates, or at least visualizing what is happening. Here's the integral calculated in Wolfram: http://www.wolframalpha.com/input/?i=integrate+%28r%5E2%28cost%5E2-sint%5E2%29%29r+drdt+t%3D%280%29..%28pi%2F2%29+r%3D%281%29..%282%29+ the...

Hello, I am solving an equation using integrating factor. I have come up to a specific point which is $$\dfrac{d}{dt} P_{02}(t) \cdot e^{(\lambda_3+\mu_3)t}=\lambda_2 \cdot P_{01}(t) \cdot e^{(\lambda_3+\mu_3)t}$$ from the previous equation, I have found $$P_{01}(t)=\lambda_1 \int_0^t...

Homework Statement http://i.minus.com/i61zvy2BbtqkI.png Homework Equations One can factor the polynomial to (x-1)^2 The Attempt at a Solution After factoring the polynomial, I integrate (x-1) given the bounds of 0 and 1. I get -1/2. The solution manual says the answer is...

Homework Statement S e^7x Homework Equations no The Attempt at a Solution Ok so I am using U-substitution for this problem but I don't know what to do next. u = 7x, du = 7dx How do I integrate e^u*du?

Hello. I was trying to solve Lagrangian equation and I manage to reduce second order differential equation that I got: \ddot{\varphi}+\alpha\frac{tan\varphi}{cos^{2}\varphi}=0; where \alpha is a constant, to first order differential equation: \dot{\varphi}^{2}+...

Homework Statement I try to solve this integral with with parameter x as a member of this scale:(-∞ , +∞) I=∫∏dx[i] exp(-0.5XAX + XB)=∫∏dx[i] exp( Ʃ-0.5x[i]a[i][j]x[j] +Ʃ x[i]b[i] ) In which a[i][j] and b[i] are components of telated matrix and vector and the first sum is on i and j ranges...

Homework Statement This problem is in Analysis on Manifolds by Munkres in section 25. R means the reals Suppose M \subset R^m and N \subset R^n be compact manifolds and let f: M \rightarrow R and g: N \rightarrow R be continuous functions. Show that \int_{M \times N} fg = [\int_M f] [...

Homework Statement Hi, I attempted to solve this question, but it did not work well. I would be grateful if you could help me. Show that an equation of the form xrys(mydx + nxdy)= 0 has an infinite number of integrating factors of the form xayb, and find expressions for a and b...

Homework Statement Find the arc length of the curve r=4/θ, for ∏/2 ≤ θ ≤ ∏ Homework Equations L= ∫ ds = ∫ √(r^2 + (dr/dθ)^2) dθ The Attempt at a Solution After some calculations, and letting θ = tanx, I now have to find ∫ ((secx)^3/(tanx)^2). I am not sure how to do this, but i...

Homework Statement I need to intergrate sin(x^3) for a sum and I don't know how to. Homework Equations The sum is (integrate)3x+Sin(x^3)+1 The Attempt at a Solution I've tried substituting u for x^3 but I don't know where to go from there considering du=3x^2.dx, which isn't...

Find $\displaystyle\int x^2J_0(x)$ in terms of higher Bessel functions and $\displaystyle\int J_0(x)$.