Integrating Definition and 940 Threads

I can see why y2 is an integrating factor, but I don't know how this answer can be derived. Do you use: \frac{N_{x}(x,y) - M_{y}(x,y)}{M(x,y)} Where M (x,y) = 4(x3/y2)+(3/y)]dx, and N = 3(x/y2)+4y dy When I try and solve this, I get a very complex integrating factor...

So I need to inegrate over a solid angle, in which every possible orientation is considered (we are doing scattering events in which we assume every possible angle is possible), thus I need to solve \int d\Omega_1 d\Omega_2 d\Omega_3 Eqn (1). Now I know \int^{2 \pi}_{0}...

Homework Statement In this problem, I am asked to find the total torque acting on a device consisting of two open half-cylinders connected to a shaft rotating in a fluid. To clarify, they are half-cylinders in the sense that they have been cut in half in the lengthwise direction and are...

Homework Statement The solid bounded by the parabolids z = 3x^2 + 3y^2 -7 and z = -x^2 -y^2 + 9 Homework Equations The Attempt at a Solution Ok so i set the two z equations into polar form and came up with 3r^2 = 7 and r^2 = 9 I thought that r went from (7/3) ^(1/2) to 3 and...

In the following problem how does -g end up becoming -g(m/g)? Isn't the derivative of -g just (-g^2/2)? http://users.on.net/~rohanlal/integfact.jpg

Okay well, I looked through my calculus notes and textbook and I can't find what to do when you are integrating a function of the type a/u where a is a constant and u is some linear function of x. I know that the integral of 1/x is ln(x) but what about when you have something like \int...

Homework Statement I want to compute \int_{C}^{}{|f(z)||dz|} along the contour C given by the curve y=x^2 using endpoints (0,0) and (1,1). I am to use f(z)=e^{i\cdot \texrm{arg}(z)} Homework Equations The Attempt at a Solution I know that for all complex numbers z, |e^{i\cdot...

Homework Statement integrate Homework Equations 1/(2x^2 + 3x + 1)[(3x^2 - 2x + 1)^(1/2)] The Attempt at a Solution

Homework Statement Indefinite integral: e^(4x+(e^4x)) Homework Equations I'm thinking integration by parts, involving UV minus integral of Vdu The Attempt at a Solution So I saw that this can be split into two: e^(4x) times e^(e^4x)). The latter is a bit complicated. I...

Homework Statement Please tell me how to integrate this... Homework Equations [(2x + 4)][(2x^2 + 3x + 1)^(1/2)] The Attempt at a Solution

Homework Statement The integral from 0 to pi/2 of 1/(1 + (tanx)^sqrt2) dx. Homework Equations trig identities? The Attempt at a Solution I tried some substitutions but it just made the problem more complicated. I also multiplied by (tanx)^sqrt2 in the numerator and denominator in...

How do you integrate xsinxcosxdx

I'm trying to follow this example from class notes. x^2 \frac{{dy}}{{dx}} + xy = 1,\,\,y\left( 1 \right) = 2 Divide through by x^2 to set it up in a form for using the integrating factor method. \frac{{dy}}{{dx}} + \frac{y}{x} = - \frac{1}{{x^2 }} I'm not sure where the minus...

Hi! I want to know how to intergrat e^(-(x^2)/2) . Someone told me to use the intergration of e^x= 1+ x + (x^2) /2!+ ...(X^n)/n! ... is that sounds right?? and if it is i got pi as an answer for e^(-(x^2)/2) , is that the right answer?

Homework Statement The sequence fn: [-1,1] -> R, fn(x)= nxe-nx2 converges pointwise to f(x)= 0, x in [-1,1]. Can you verify the following: limn->\infty (\int^{1}_{0}fn(x)dx) = \int^{1}_{0} (limn->\infty fn(x))dx Homework Equations Theorem: If fn is continuous on the interval D for every...

Homework Statement I am having a problem integrating in a WKBJ semi-classic integral. Well it's this : I have to integrate \int_{0}^{\sqrt{m}E}\sqrt{E-\frac{x}{\sqrt{m}}}dx Homework Equations Actually I don't have that much experience at integrating, so could you somehow show me how to...

Homework Statement Homework Equations The Attempt at a Solution Homework Statement Homework Equations u = 1+tant du = sec^2(t) dt dt = du / sec^2(t) The Attempt at a Solution It seems like I should be using substitution in the equation, however the exponent is...

Homework Statement I want to deal with this int((5+10y^4)dy/(y+2y^5)) Homework Equations integration, substitution, partial fractions? The Attempt at a Solution I tried a bunch of random things. I think it hs to do with substitution because if I make u=y+2y^5, du/dy=1+10y^4...

Homework Statement how do i integrate v^2 / v^2 + 4 Homework Equations i understand this has something to do with arctan but if i use u substitution to let v=(u/2) so (on the bottom) it becomes (1/4)(1+(v/2)^2) there's still a v^2 on the top which the u substitution does not...

Homework Statement Integrate 1/(x2 +11x +29) Homework Equations The Attempt at a Solution I'm doing something wrong, but can't figure out what... Complete the square so that the denominator equals (x+2)2+25 Then divide by 25: ((x+2)2)/25 + 1 Move that 25 into the squared...

Homework Statement How would I begin to integrate ln(t+1) from 0 to e^2x? Homework Equations d/dx[log base a of u]=1/(lna)u du/dx Can the original equation be manipulated to use this derivative? The Attempt at a Solution Not sure where to start.

I can't figure out how to this integral. I keep coming up with the wrong answer. Can someone please show me a detailed solution?

Homework Statement Consider the Sun to be a sphere of hydrogen gas of uniform density equal to its average density (1440 kg/m3). a) Integrate the equation of hydrostatic equilibrium for dP/dr from the Sun’s radius to the core to estimate the central pressure in Pa and in atmospheres...

Hi, Can someone tell me how to integrate functions which have a branch point and a pole (of order > 1) on the x-axis. Specifically, I ran into the following problem while playing around with contour integrals, which has a double pole at x = -2 . I tried to do this with a keyhole contour...

If an odd function has an infinite discontinuity in its domain, can it be integrated (such that a convergent finite emerges) with that domain included? For example: \int_{-1}^2 \frac{1}{x^{-3}} dx. Intuitively, it can be simplified to \int_1^2 \frac{1}{x^{-3}} dx and thus the infinite...

I was given the following ODE to solve and it seemed simple enough. However, after you have used the integrating factor the integral is not integratable. y' = (1+x^2)y +x^3, y(0)=0 Find y(1) if y(x) is the solution to the above ODE. So I put it in the proper form of: y' + (-1-x^2)y...

Hi, I want to calculate the potential energy between two opposite charges (a dipole) and I know how to integrate Coulomb’s law in the polar form, i.e. in terms of “r” \[...

revising for an exam and have the question let I=∫lim ∞ to 0 e-x2 dx. since x is a dummy variable here, replace it with y to get a second expansion for I. Multiply these two together to get a double integral for I2. Transform into polar co-ordinates noting that dxdy corresponds to r dr d♂. Carry...

does anyone knw the code for how to produce the d slash notation in the integration measure for momentum space? Where (d slash)^n X=(d^n)X/((2pi)^n). Basically all i want to do is replace the h: \hslash with a d.

Homework Statement Integrating -e-4tsint Homework Equations Our tutor suggested we did this by integrating by parts in a cyclic fashion and things would cancel out The Attempt at a Solution Taking u = sint t; thus u'=cost And v'=-e-4t; thus (1/4)e-4t \int-e4tsint =...

Hi, How do integrate this? I wish to see it step by step and I'm glad for any help i can get. \int_{ \vec{r}\in{A}} \frac{ \vec{v}+ \vec{\omega}\times\vec{r}}{| \vec{v}+ \vec{\omega}\times\vec{r}|}d^{2}r where A is area of disk with radius R.

Homework Statement before we start, i don't know how to do the integral sign, so we'll use [ I need to integrate [ e^(-3x) / 1 + e^(-3x) Homework Equations I've always had trouble with doing integration with e The Attempt at a Solution I used u=1+e^(-3x) du = -3e^(-3x)...

Homework Statement Find the gerneral solution of the differential equation below: dy/dt=(-y/t)+2 Homework Equations none The Attempt at a Solution my solution by using integrating factor: 1.find the homogenous solution first dy/y = -1/t dt you get ln(y) = -ln(t) when...

Hello, I have a power series, and a problem with an integration with it, I don't understand why I should integrate it from zero at one point. I have attached a detalied explanation of the problem. http://img79.imageshack.us/img79/5156/powerseriespt4.jpg Any help would be greatly appreciated.

What's the proof of this fundamental theorem? Let (X,B,u) and (Y,C,v) be sigma finite measure spaces, Let f in L1(X,B,u) and g in L1(Y,C,v). Let h(x,y)=f(x)g(y). Then, h is in L1(XxY,BxC,uxv) and \int hd(u\times v)=\int fdu \int gdv should be an easy application of fubini,but i really have no...

The question asks me to integrate x^2 sin x dx and then use it to find the exact value of the integration of abs ( x^2 sin x dx) with upper limit of pi/2 and lower limit of -pi/2. I have found the integration of x^2 sin x dx which is -x^2 cosx + 2xsinX + 2 cosx + C but after putting in the...

Hello, I tried this in analysis but maybe it is a more topological question. If given a function f on R such that \int_R f(x)dx = 1 and is decreasing and 1-lipschitz, show that the function g(y) = min{x,f(x)} where y = x-f(x) and x>=0, also satisfies \int_Y g(y)dy=1. I really would...

I can't seem to integrate this correctly. I only need the half loop integration, as i have the correct integration for the infinite lines. Homework Statement We start with the top half of a half-loop of radius R, centered at the origin, with infinite line segments traveling in the +/- x...

Homework Equations Need to integrate x^2/((x^2-1)^(1/2)). The Attempt at a Solution I first broke the equation into (x^2-1)^(1/2) + (x^2-1)^(-1/2) Hence Integral (x^2/((x^2-1)^(1/2))) = Integral((x^2-1)^(1/2)) + Integral((x^2-1)^(-1/2))) Further on Integral((x^2-1)^(1/2)) is an...

I am a little bit confused about dealing with integrals around singularities because my professor seems to treat some situations more rigorously than others. We talked this integral and said \int_{-\infty}^{\infty}\frac{1}{x^3} dx = undefined This seems a little bit unintuitive to me...

Homework Statement By multiplying the integrand sec x dx by \frac{tan x + sec x}{tan x + sec x} find the integral of sec x dx Homework Equations d/dx sec x = tan x.sec x d/dx tan x = sec^2 x The Attempt at a Solution sec x dx(\frac{tan x + sec x}{tan x + sec x}) => \frac{tan...

Hi folks: Question for you guys. I've generalized a question that keeps coming up in class...but that keeps going unexplained. This is a somewhat involved problem which requires integrating force to find work. Thing is, force is always integrated as a function of position NOT time. This type of...

Homework Statement I have a couple of questions about some intriguing looking equations. Firstly, I have to integrate: \frac{sin\theta}{cos\theta} d\theta Is there an answer to just dividing them? because sin/cos = tan, but that doesn't seem to help? Secondly, I have to integrate...

Homework Statement I'm doing a problem on Gaussian functions (there are other constants to make it interesting, but I've removed them here): 1. \int_{0}^{x} e^{-x^2} dx 2. \int_{0}^{x} x e^{-x^2} dx 3. \int_{0}^{x} x^2 e^{-x^2} dx We know that erf(z) =...

\int^{1.5}_{0}\int^{1.5}_{0}\int^{1.5}_{0}\frac{1}{x^2+y^2+z^2}dxdydz I tried converting this to spherical and only integrating over a quarter of the octant but with no luck. Can someone please point me in the right direction. Thanks!

Integrating Natural Log Function using "Integration by Parts" Method Homework Statement The problem says to integrate ln(2x+1)dx Homework Equations I used u=ln(2x+1); du = 2dx/(2x+1); dv=dx; v=x The Attempt at a Solution So, I integrated it using that (above) 'dictionary' and I...

Homework Statement Separable equations dy/dx = y * e^(sinx +cosy) and dy/dx = sin(x^y) The Attempt at a Solution For the first problem, I did dy/dx = y * e^(sinx) * e^(cosy) and separated. However, I can't figure out how to integrate e^(sinx)dx on the right. Did I do somehting wrong? I...

How do I integrate (e^ax)sin(bx)

I was working on this problem \int{\frac{x^3}{x^{2}+1}}dx I at first tried to use one of the inverse trig functions but couldn't get the form to match...should I try to use log properties...making the denominaor u and trying to get the numerator 1?

please... i need a help in integrating the partial fractions i can't proceed to the integration part if i don't understand the patter in finding the constant... that is... if the given is: ʃ ( (x^5+1) / ((x^3)(x+1)) )dx then; ʃ ( x-2 + ( 4x^3+1 ) / ( x^4 + 2x^3) ) ʃ ( x-2 + (...