Integrating Definition and 971 Threads

I'm having real problems integrating a natural log. The problem I have been set is (where S = integration sign) S (x - 2) Ln(3x) I'm trying to use the integration by parts rule but keep getting the wrong answer and I think it might be to do with the natural log. I have used f(x) =...

\int x^xdx After calculus today, our professor casually asked us to integrate the above problem. Most of us stated DNE (does not exist), or possibly x+1 / x+1 . He stated that both of these solutions were incorrect and than challenged us to write a paper on the subject which seemed...

Hello everyone I'm stuck with a problem from Simmons (not HW). The problem asks to solve the following equation by finding an integrating factor (xy-1)dx + (x^2 - xy)dy = 0 I found by hit and trial that there can be no integrating factor that is a function of x alone or y alone. So how...

Homework Statement no specific problemsHomework Equations x center of mass = moment about y/total area y center of mass = moment about x/total area The Attempt at a Solution ok, so I am in AP calculus, and since the AP testing has ended, we've done some random topics, such as centroids of...

Hey, I am in high school AP Physics/Calculus and my group needs to come up with a project that involves both the use Physics and Calculus. We are willing to research and do anything. Does anyone have any interesting topics that they could share with us. By the way, we CANNOT do a project on...

Need help, soon please! Integrating I am struggling to integrate this function since last night but,it seems like it is a dead end doing it. how would you integrate this function integral x^n e^(-x^(n-1)) dx i tried the parcial method, and went like this integ x^(n-2) x^2...

Homework Statement Final round I promise! Is there some sort of trick that can be applied to the following equation so that it is easier to process? \frac{dy}{dt}=\frac{1}{t+y},\:y(-1)=0 The Attempt at a Solution Somebody told me that the equation can be made easier by...

Homework Statement y' (1+e^t) + e^ty = 0 How do I get it in the form y' +f(t)y = f(p) That is how do apply algebra to this so it is in the proper form to process it? The Attempt at a Solution Kind of hard to post my attempt. I can move the y' (1+e^2) to the right side then divide both...

Homework Statement y' + 2ty = t^3 Homework Equations Integrating factors and variation of parameters The Attempt at a Solution Ive solved for m M = e^{\int 2t\,dx} M = e^t^2 (this is e^t^2, but doesn't look like it in latex) I multiplied both sides by M (e^t^2)(y') + (e^t^2)(2ty) =...

Is there a way other than trial and error to tell whether an integrating factor h is a function of x only, y only, or of x and y?

I want to integrate (cos(x))^4, but I can't find a formula for (cos(x))^n in my collection. What is the way to integrate this?

From an example in my book: Int Int (2x) dxdy over R = 0 (R is the circe x^2+(y-1)^2=1) How can one make this conclusion without integrating?

Hi. I've been struggling with this for hours and not getting anywhere even after a hint from a teacher. I have to integrate (indefinite integral) v / (1+cv²) where c is a constant. The hint the teacher gave was that the integral of 1 / (1+v²) is tan^-1(v), but I can't see how to use this...

How would you integrate this equation?

Ok well The integral is : \int \frac{1}{\sqrt{1-x^2}} \frac{1}{\arcsin x} dx. I can tell by inspection, it being of the form f'(x)/f(x), that the answers ln (arcsin x), but I was hopping Integration by parts could do it for me as well. But here's my Problem: u=1/(arcsin x) du=(-1)/...

Homework Statement How do you integrate a product of two trigonometric functions of x, when the argument is different, ie: what is the integral of sin x cos 3x I ought to know this, but don't seem to be able to do it. Thanks in adv! Homework Equations The Attempt...

I don’t know how to integrate the Maxwell-Boltzmann distribution without approximation or help from Maple. Given the Maxwell-Boltzmann distribution: f(v) = 4*pi*[m/(2*pi*k*T)]^(3/2)*v^2*exp[(-m*v^2)/(2*k*T)] Assuming a fixed temperature and mass, one can simplify this equation: f(v)...

I have to integrate over the northern hemisphere of a sphere. The answer states that the integration bounds for r is 0 to R, for theta it's 0 to pi/2, for phi it's 0 to 2pi. What I don't understand is why theta doesn't go from 0 to 2pi. If I had to set this up, I would have theta going from 0...

Homework Statement I'm being dead thick, but I can't remember how to integrate an exponential function. \int x^3e^{-\alpha x^2}dxHomework Equations The Attempt at a Solution I reckon that this shouldn't be too complex, but I've totally forgotten how to go about this question. The x^3 term means...

Homework Statement To find the voltage-current relationship of a capcitor, integrate both sides of i = C(dv/dt) The Attempt at a Solution In the book they say, v = (1/C)(The Integral from -tve infitity to t) of i dt. or v = (1/C)(The Integral from tnot to t) of i dt + v(tnot)...

I know that \int \tan^{2}x dx= \int \sec^{2}x-1\ dx = \tan x - x + C but i don't completely understand how this is derived. Because of this lack of comprehension, I have no idea what to do with \int \sec^{4}5x\ dx. I went from there to get: \int \sec^{4}5x\ dx= \int [\sec^{2}5x]^{2}\ dx= \int...

I Just want to know if this is how this should be done.. \frac{dy}{dx} = \frac{3y^2}{x} dy = \frac{3y^2}{x}dx dy = 3^2 x^-^1dx \frac {1}{3} \int \frac {dy}{y^2} = \int x^-^1dx \frac {1}{3} ln| y^2| = ln | x | + C because I forget how to integrate the polynomial...

Homework Statement Find the integral of: Homework Equations x^2 . sinx dx (With upper and lower limits of pi and 0 respectively.) The Attempt at a Solution Integrating for the first time: -x^2 . cos x + 2 [integral of] x . cosx dx After integrating a part of my first...

Homework Statement solve the following equation using method of intergrating factors: Homework Equations dy/dx = y + cosx - sinx The Attempt at a Solution i think i have to get it in the form dy/dx + r(x)y = f(x) but i can't see how, if i multiply or divide by a factor i...

Find the two integrals: \int_0^{\infty}\frac{e^{-\alpha x^2}}{x^2+1}\sin(\alpha x) \, dx \int_0^{\infty}e^{-\beta^2t}\cos(\beta x) \, d\beta Any hint?

Suppose you have an equation: M(x,y) dx + N(x,y) dy = 0 I have heard that there always exists an integrating factor u(x,y) such that the partial derivative of uM with respect to y equals the partial derivative of uN with respect to x. But somewhere in the back of my mind I remember that...

Hi, i have a problem which is confusing me :confused: Question: Given that \int_{0}^{\infty}e^{-ax^2} dx = \frac{\sqrt{\pi}}{2\sqrt{a}} What is (i) \int_{0}^{\infty}e^{-ax^2} x^2 dx (ii) \int_{0}^{\infty}e^{-ax^2} x^3 dx (iii) \int_{0}^{\infty}e^{-ax^2} x^4 dx It tells me...

I am trying to integrate the the normal vector to the surface of a hemisphere but am having some trouble. I am pretty sure that the x and y components will cancel out, and that the z component in spherical coordinates is R*Cos[theta] but for some reason I am having trouble really understanding...

The task is to find one primitive function to: (4x-3)^2 This was quite straightforward. Or so I though. It can easily be turned into 16x^2 - 24x + 9 and then integrated to \frac {16x^3}{3} - 12x^2 + 9x choosing C = 0 Then I started to think. Couldn't this be integrated...

I have the expression \int{x(\ln{x})^3dx} I thought I had a quick way to integrate by parts but it turned out that I had accidentally evaluated \int{x\ln{x}dx} instead. Revisiting \int{x(\ln{x})^3dx}, I wanted to start by making a strange substitution, wherein u=ln(x), du=1/x dx, and x=e^u...

Could someone please show me the steps of integrating this integral? -1/4[e^(-2t)csc(2t)dt]

Here is my problem: I need to integrate: (\frac{sin \alpha z}{\alpha z})^2\frac{\pi}{sin\pi z} around a circle of large radii and prove: \sum_{m=1}^\infty(-1)^{n-1} (\frac{sin m\alpha}{m\alpha})^2 =\frac{1}{2} I'm kind stumped. I've been looking at books for a while...

I have problems with integrating this... :( \int_{0}^{x}\frac{1}{\sqrt{a^2 - b/x}}dx I have tried substituting 1/x with u and so on... But it doesn't seem to work :( Thanks in advance!

Here is the question from the book: By integrating the binomial expansion, prove that, for a positive integer n, \frac{2^{n+1} - 1}{n+1} = 1 + \frac{1}{2}\binom{n}{1} + \frac{1}{3}\binom{n}{2} + ... + \frac{1}{n+1}\binom{n}{n} ------------ So I integrated both sides of the following...

Ok, so it's been a while since I've had to integrate anything, much less something like this. \int \frac{1}{n(1 + \ln{n})^{2/3}} dn I'm thinking u substition for ln(n) and then du becomes 1/n? But, since the ln(n) is in the denominator of a fraction raised to a power, wouldn't that mess...

How does one integrate \int_{}^{} \frac{e^x}{x}dx I could expand it using a Laurent series and than integrating term by term but are there more elementary methods?

Find the integral of: f(x)g'(x)dx from zero to ten. If f(x) = x^2 and g has the following values on the table at x=0, g(X)=2 at x=2, g(x)=2.7 at x=4, g(x)=3.8 at x=6, g(x)=4.6 at x=8, g(x)=6.0 at x=10, g(x)=6.7 I know that I have to approximate the integral by finding the average...

Got the eqn dy/dx=x(1-y) and it can be solved both linear and separable methods.(Linear method being using a integrating factor) Problem I am having is that with this two methods i get two different (yet similar answers) and was wondering if you can see my problem with this two methods I am...

I just discovered this forum: very very nice! And here's my first question: An exterior p-form is a multilinear antisymmetric map from p copies of a vector space (in particular, a tangent space located at some point P of a manifold) to the reals. Now what could it mean to have an integral of a...

when you integrate the energy density (from electromagnetic field) times the differiential volume of the whole 3D space for a photon...would you get the energy of it? E=hf ? one more question... if there is a positive charge in 3d space... when i integrate the electromagnetic energy density...

Hello. This is more a Mathematica question really, but here it goes anyway. As a consequence of some calculations on high energy physics, I need to integrate an expression that involves a Levi-Civita tensor contracted with four FourVectors (I'm using the FeynCalc package). I'm guessing the...

Dear All, I have a moderate knowledge of mathematics and need help on an integration question. How would I go about integrating a step function: H(K - Z), when the integral is from K=Z to infinity. Please advise, your help would be much appreciated. Suz

Hi, I'm having quite a bit of trouble with this topic. Here's one of the first problems, I don't really understand the method in the book, if someone could show me an easy route, it would help. \int_{0}^{1} \frac {2x+3}{(x+1)^2}dx Thanks

I'm solving the following equation in the unit square using finite differences: epsilon(u_xx+u_yy)+u_x+u_y=0, where epsilon is a singular perturbation parameter. I need to use domain decomposition to isolate the corner singularity in the outflow corner. My subdomain in this corner is a...

Gravity - Integrating General Relativity with "Gravitons" Every time I read about the hunt for gravitons I never see an explanation of how they will actually produce their effect. Maybe "integrating" is not the best word, but how will gravitons, if proven to exist, lead to the warping of...

What approach should be used to solve the following DE: dy/dx= (-2x+5y)/(2x+y) Find an integrating factor and solve it as an excact equation? Thanks.

Find the antiderivative of: -2x (1-x^2)^(1/2) That's -2x over all of that... Bleh, i suck at code. But anyway.. I just started integrals, and this is confusing for me... Is there a product or quotient rule in integrals like there is in derivatives?.. if not? how do you work...

I am trying to solve this Fourier problem where I have to integrate ∫f(x) * exp(-i§x) dx from -∞ to ∞ , where f(x) = exp(-sgn(x)) I tried breaking the function into two pieces where x is from -∞ to 0 and from 0 to ∞ where f(x) would then be exp(x) and exp(-x) and integrating two functions...

Hello, I have a few questions! I need clarification on certain points that were not very clear in my calculus book. ---------- Question 1: I know that \int e^{ax} dx = \frac{1}{a} e^{ax} But how do you integrate \int e^{ax^2} dx ? ----------- Question 2: I know that...

integrate with respect to x: (sinx)^3 * cosx i have no idea where to start, can anyone help me? I've looked at differentials of other trig functions but i can't see any that would help :mad: