Integrating Definition and 940 Threads

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...

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

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:

integ [e^x / (1 + e^2x ) ]dx.can someone show me how to solve this by using 1 / (1 + x^2 ) formula?? pls...

I am having a heck of a hard time with this integral... I have tried everything what I can think of: \int \! \left( {e^{x}}+{e^{-x}} \right) ^{-1}{dx} I tried integration by parts... I ended up getting \left( {e^{x}} \right) ^{-1} even thought the right answer, according to Maple and my...

Hello everyone I understand how to solve exact equations, but what happens when they arnt' exact? I'm confused on what I'm suppose to do! Does anyone feel like explaning hte process to me, if given an integrating factor/> or give me a website? Here is my problem: Check that the equation...

Hey everyone, I need to find an integrating factor of the form x^n*y^m, to solve a differential equation i have... however i do not know the process to solve for an integration of this form.. .any help?? Thanks Steph

Hi I have the following problem: To calculate the fine structure energy corrections for the hydrogen atom, one has to calculate the expectation value for (R,R/r^m), where R is the solution of the radial part of the schroedinger equation (i.e. essentially associated laguerre polynomial) and...

Please help me to solve the following questions using \int [f(x)]^nf(x)=\frac{[f(x)]^{n+1}}{n+1} \int tan {2x} dx

Could someone please point me forwards again. By integrating the following equation twice... \frac{1}{x^2}\frac{d}{dy}(x^2 \frac{dx}{dy}) = 0 I tried integrating by parts but came to a sticky end. many thanks skook

I'm trying to perform the following integral \pi \int\limits_0^\pi {e^{2x} } \left( {\frac{1}{2} - \frac{1}{2}\cos 2x} \right)dx I split the integral and temporarely ignore the Pi so that I get \frac{1}{2}\int {e^{2x} dx} - \frac{1}{2}\int {e^{2x} \cdot \cos } \left( {2x} \right)dx...

for the equation, (a+1)ydx+(b+1)xdy=0, i am wondering how to get (x^a)(y^b) as an integrating factor~ the following is my work: (1/F)(dF/dx)=(a-b)/[(b+1)x] => F=cx^[(a-b)/(b+1)] why doesn't that method work?

for the question, siny+cosydy=0, i want to find an integrating factor. my work: (1/F)(dF/dx)=(1/cosy)(cosy+siny)=1+tany =>lny=x +xtany +c` => y =ce^(x+xtany) however, the question wants the integrating factor to be e^x... why?

Howdy, I've read this forum for some time, however this is my first post. I am attempting to solve this ODE. I am looking to find an integrating factor, then solve. I have attached the link to the problem set if my input here is ambiguous. Number 4d. Thank you kindly for any help you might...

Ok, so we have \int_{0}^{1}\left(\sin{2x}*\cos{2x}\right)dx Using the double angle forumla we change the integrand (1/2)\int_{0}^{1}\left(2*\sin{2x}*\cos{2x}\right)dx which converts to (1/2)\int_{0}^{1}\left(\sin{4x}\right)dx This is where I run into trouble... I'm trying to...

how do you spot that a D.E. needs an integrating factor, besides experience?

Hello, i am now in the process of integrating m(d^2x/dt^2)=-kx which i know i will have to do twice in order to obtain the general solution to simple harmonic motion, x= Acos(wt+c) c=phi but I'm just having problems with the second derivative of acceleration (d^2*x/dt^2) when it comes to...

While integrating the function f(x) = \frac{1}{x ^ 2}, I came across something I don't understand: \int \frac{1}{x ^ 2}dx = - \frac{1}{x} + C Let f(x) := \frac{1}{x ^ 2} f(x) > 0, \forall x \in \mathbb{R} \int_{-1}^{1}f(x)dx = -1 - (-(-1)) = -2:confused: Why this happened? :confused: It's...

hi felles. I am trying to find what is the volume of the y=\frac{a}{x^2}+b is when it is rotated in y-axis. The values of a is 1 and b is -1. max hight is 3 and min is 0. I was trying to integrade and ended up with V=\frac{-Pi}{y^2+2Y+1} where y is 3. Is this right? I did a U...

\int \frac{\cos^5(\theta)}{\sin^4(\theta)} d\theta Anyone mind sparing a little hint for this tricky devil? I can't even get started on it. \cot^4(\theta)\cos(\theta) dosn't seem any better either. I've tried using identities but I end up with nastier ones?

\int_0^\sqrt{6}}e^{-x^2}\frac{x^2}{2} should i use a u-substitution or integration by parts?

Q. By finding a suitable integrating factor, solve the following equation: \left( {x + y^3 } \right)y' = y (treat y as the independent variable). Answer: Exact equation is y^{ - 1} \left( {\frac{{dx}}{{dy}}} \right) - xy^{ - 2} = y leading to x = y\left( {k + \frac{{y^2 }}{2}} \right)...

Hello everybody I'm very much interested in the thread about "Feynmans Calculus" (having read the books, too). The problem is I don't understand quite some of the stuff, because I don't have the necessary fundamental knowledge. So I thought to confront you with some lower level questions...

For eg is there a way to find IF for pydx +qxdy +x^my^n(rydx+sxdy)=0

I am going to be gone all day tomorrow at a conference track meet and am unable to ask my teacher how to do integrating factors and differential operators. I leave tomorrow at 9:15 am and was hoping to have some examples to take with me to study. If someone could help me walk through a these...

Hi guys, I need a bit of help with this. I've got an op-amp and the standard formula: V_{out} = -\frac{1}{RC}\int V_{in} dt And i need to integrate a square wave from it in order to determine some capacitor/resistor values to get an output amplitude of 5V and freq 200Hz (triangle wave)...

Help, I'm trying to find the hypervolume of a hypersphere and I'm stuck on this: V^4= 2(\frac{4\pi} {3}) \int_0^r (\sqrt{r^2-x^2}) ^3 dx I don't know how to do the integration, and I can't expand the (\sqrt{r^2-x^2}) ^3 The answer should be \frac{\pi ^2}{2}r^4 Please help, thanks

Ok, I have to integrate this [int a=0 b=3] 1 / sqrt[abs(x-2)] dx what should i do ? do the improper integral of 1/-(x-2) and 1/(x-2) ?

I have the following Integral \int ^1 _0 \int _0 ^\sqrt{1-x^2} \int _0 ^\sqrt{1-x^2-y^2} \frac{1}{1+(x^2)+(y^2)+(z^2)} dzdydx (With the limits working properly!) Converted to spherical Cor-ordinates, I have \int ^\frac{\pi}{2} _0 \int _0 ^\frac{\pi}{2} \int _0 ^1...

Integrating dx/dv^2 ?? i'm trying to figure out an example in my physics book but i don't quite understand the maths. [tex] \int \frac {dv} {v^2} = - \frac {1} {v} [\tex] how does this happen?? looking at the basic antiderivative formulas section in my maths book, it says that...

i noticed that if i integrate 2 \pi r i get \int 2 \pi r dr=\pi r^2 i figured its because the area of a circle can be seen as the sum of circumference's of circles with radius 0 to radius r i was thinking if the half volume of a ball also be seen as made from the sum of areas of circules...

Determine the integral: y = \int_{0}^{1} 1/(u^4+1)du and y = \int_{0}^{1} 1/(u^5+1)du and y = \int_{0}^{1} 1/(u^6+1)du

This last part of an AP questions is giving me some trouble, mostly because i involves integrating and i never took Calculus. Part D: The dart is now shot into a block of wood that is in a fixed place. The block exerts a Force F on the dart that is proportional to the dart's Velocity V and in...

\int cos(u^2)du Is it doable at a Calc One level? I tried by parts and got to \int cos(u^2)du = ucos(u^2) + 2\int(u^2sin(u^2)du but I am having a brain fart as to hwo to advance, trying again by parts.