Integrating Definition and 940 Threads

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 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...

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 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 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 $\displaystyle\int J_0(x)$.

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 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...