Integrating Definition and 971 Threads

Hi, I tried to solve this by using the integrating factor technique \begin{cases} dy/dt +10y = 1 \\ y(1/10) = 2/10 \end{cases} So p(x) = 10t \rightarrow e^{10t} e^{10t} \cdot \frac{dy}{dt} + e^{10t} \cdot 10y = e^{10t} This part is confusing to me, i have two different variables...

Homework Statement Find \int\frac{x+2}{x^{2}+2*x+10}*dx You are given that \int\frac{du}{u^{2}+a^{2}} = \frac{1}{a}tan^{-1} \frac{u}{a} + C for a not equal to 0 Homework Equations None. The Attempt at a Solution I'm not entirely too sure how to go about doing this. I first thought of...

Hi, Could someone help me see how the solution of the equation \frac{1}{\mu} \frac{\partial p}{\partial z} = \frac{1}{\rho} \frac{\partial}{\partial \rho} (\rho \frac{\partial v}{\partial \rho}) is v = \frac{1}{4\mu} \frac{\partial p}{\partial z} \rho^{2} + C_{1}ln(\rho) +C_{2} Thank...

Homework Statement I recently came across this integral while doing a problem in electromagnetism (I'm not sure if there exists a nice analytic answer): \int_{0}^{\pi}P_m(\cos(t))P_n(\cos(t)) \sin^2(t) = \int_{-1}^{1}P_m(x) P_n(x) \sqrt{1-x^2}, Homework Equations P_m(x) is the m^th...

Intergrate 2^x ... lol? How would I even go about this? This is not a homework question, but I'm practising for exams.

Homework Statement All that is provided can be found through the following link: http://img33.imageshack.us/img33/6343/question2q.jpg Homework Equations No specific equations pertaining to solving double integrals. The Attempt at a Solution Ok, so I know that we cannot...

Homework Statement I'm confused about integrating something like \int\frac{1}{u} Sometimes the answer seems to be ln|u| and sometimes just ln(u), and I wasn't sure why it is different from problem to problem. (after subbing u back in; I'm using the u-sub method) It looks like the answer should...

Hi! This is my first post. I have a question of cosmological importance - literally and figuratively. The Standard Model is the most accepted theory of (almost) everything, yet is unable to make sense of gravity. String Theory can explain it all theoretically through quantitative...

Hi, Can anyone suggest how to integrate the following function, in which all the c's are constants: c1 * x^c2 * ln [ -1 + sqrt (1 + c3 * x^c4) ] Much obliged!

Is there a method of integrating factors for differential equations of power 2 or higher?

Homework Statement find the length of the cardiot r = 1+cos(Θ) I'm going to use { as the integral sign all integrals are definite between 0 and Pi Homework Equations L = 2 {sqrt[(r^2(Θ))+(dr/dΘ)^2]dΘ The Attempt at a Solution L=2* {sqrt[2+2cos(Θ)] dΘ I'm having a really hard...

Homework Statement Find general solution of equation (t^3)y' + (4t^2)y = e^-t with initial conditions: y(-1) = 0 and t<0 book answer gives y = -(1+t)(e^-t)/t^4 t not = 0 Homework Equations The Attempt at a Solution (t^3)y' + (4t^2)y = e^-t get integrating...

Homework Statement C is triangle (0,0), (4,0), (0,3). R is the enclosed region. Compute the following integral, where n is the outward pointing normal: \int_{C} \left(4x-y^{2}\right)n^{1}ds where n^{1} = \widehat{i} \cdot \widehat{n} Homework Equations The Attempt at a...

Homework Statement Derive an equation for an objects velocity as a function of time Homework Equations i have that a=-(kvo/m) The Attempt at a Solution so i get dv/v=-(k/m)dt then i get 1/v= -kt/m +C and then I am stuck

Homework Statement \int\int y \sqrt{x^2+y^2}dx dy Homework Equations x\geq 0, y\geq 0, x^2+y^2 \leq 4 The Attempt at a Solution first of all, what are the limits of integration rearranging x^2+y^2 \leq 4 you get x = 2 - y this would be my limit of integration for the inner integral yes...

So there's this equation: x^2 y^2 dx + (x^3y-1)dy It has to be solved with the integrating factor method, so I get this: \mu(y) = e^{\int \frac{dy}{y}} = e^{\ln{|y|}} = |y| My question is, what do I do with the absolute value bars? If I just drop them and multiply the entire equation with...

hi, can anyone tell me how the following will be integrated: (where all letters except 'x' are constants) x/(ax^3 + bx -c ) i tried to simplify the integral using partial fractions, but ended up with: p/(x-q) + (rx +s)/(tx^2 + ux + v) obviously, the first term is trivial, but how...

the integral \int_{-\infty}^{\infty} \! f(t)*\delta (t-t_0) * \delta (w-w(t)) \, dt is?? can be \delta (w-w(t)) * f(t_0) ?

Homework Statement I just can't crack the integral of (sin(x))^6 for some reason. What is the exact solution to this? This is not really a homework question, as an immediate reference to an integral table would be sufficient. But I just need it right away. Thanks. Homework...

Homework Statement the curve y= sqrt(x² +1) , 0 ≤ x ≤ sqrt(2) is revolved about the x-axis to generate a surface. Find the area of the surface of revolution. Homework Equations A = 2π ∫ f (x) * sqrt[1+f ' (x)] dx The Attempt at a Solution I've gotten down to 2π ∫ sqrt(2x²+1) dx...

\int|x|2 with respect to the vector x in the unit ball in Rn-2 I'm dealing with volumes of unit balls in Rn and after applying a change of variable to the last 2 components and Fubini's Theorem, I get that integral and can't find a way to integrate it. Any help on this?

Hello, I have just integrated over one variable, x and have now got a delta function \delta(m) where m = constant * (s-s') now I have to integrate over either s or s' but I am a bit confused since if I integrate over say s then the delta function depends on s. Hope I have explained clearly...

Homework Statement Needing to integrate 3ye^3z dz Homework Equations The Attempt at a Solution I believe you use u substitution and u=3z du=3dz Then you get yze^3z. Is this correct?

Homework Statement Revolve the region bounded by x=0, x=1, y=0 and y=x^5 about the y-axis use shells to find the volume I know how to set up the integral I just don't know where I'm integrating from. Is it from 0 to 1?

I couldn't figure out what to do with this type of integration \int (a x^{2}+ bx +c) ^{\frac{m}{n}}dx here m, n are integer numbers. Integration limit -∞ to +∞. Will Binomial expansion work? Please give me some clue.

Integrating exp(x^2) like gaussian integral?? Hi, I can't solve this integral \int^{1}_{0}\\e^{x^2}\\dx Can I solve this integral like gaussian integral? Please help me Thanks.

Homework Statement ∫ e^(\pix^2) dx, with limits -∞ to ∞ Homework Equations ∫∫ dxdy = ∫∫ rdrdθ The Attempt at a Solution Hi, here's what I've done so far: Introduce a dummy variable y to get ∫∫ e^\pi(x^2 + y^2) dxdy, with limits -∞ to ∞ for both dx and dy...

Homework Statement \int 59x(cos(x))2 dx Homework Equations The Attempt at a Solution I tried doing integration by parts with u= (cos(x))2 and dv= xdx v= \frac{x^2}{2} However this didnt get me very far can some one tell me what the first step or two are.

I am a little confused here. If the integral of f'(x)/f(x)= ln|f(x)| +k then say the below equations which are the same give different results? 2/(2x+2) The top is a derivative of the bottom, so the integral is ln|2x+2|+k 1(x+1) This is the same as the first equation. The top is also...

Hey I'm having problems trying to integrate my function func1 in MATLAB. Really don't know where I am going wrong so would really appreciate if anyone could help. The code I'm using is below, thanks: Function Mfile: function [ f1 ] = func1( E, Delta, kB, Temp ) %func1: calculates...

I'm supposed to be Integrating 1/(4+x^2)^2 dx using trigonometric substitutions, but I do not know how to get started with this one. Am I supposed to rewrite this as 1/sqrt((4+x^2)^2) and then use the reference triangle? I've tried expanding the bottom, but that doesn't get me anywhere...

Homework Statement Find a power series representation for the given function using termwise integration. f(x) = \int_{0}^{x} \frac{1-e^{-t^2}}{t^2} dt Homework Equations The Attempt at a Solution Well, I figured I could rewrite it like this using the Maclaurin series for...

Finding the integrating factor (ODEs) [Solved] Working on this problem, I can't figure out why we take the derivative of \mu with respect to y, and what to do when our integrating factor is a function of both x and y. In the case below, it ended up being separable, but what can you do if it's...

Hi, this isn't a homework question, I'm just curious about this. I am wondering what the correct notation is for the integral of F(x). For example, integral of f''(x) = f'(x) + c integral of f'(x) = f(x) + d integral of f(x) = F(x) + e integral of F(x) = ?? I feel silly for not...

Homework Statement I need to integrate the equation shown below in the picture. It is a polar coordinate function with r(double dot) being the acceleration radial and theta(double dot) being angular acceleration. I need to integrate with respect to time, to get equations for r(dot) and r...

Homework Statement Calculate \int _{\mathbb{R}^{3+}} V(\textbf{r} ) d\textbf{r} where V(\textbf{r})=\frac{1}{r},\ \ r=||\textbf{r}|| The Attempt at a Solution I'm guessing \textbf{r}=x \textbf{i} + y \textbf{j} + z \textbf{k} so r=\sqrt{x^2+y^2+z^2} and d\textbf{r}=...

Hi guys, this is my first post but have read the forums for a long time - a quick search didnt bring up anything that could help me. So i was wondering if someone could please explain something to me. I have a differential equation (excuse the pictures, I don't know how to use the equation...

Ok, here's the question, have patience with my terrible latex skills... Homework Statement The equations of constraint of the rolling disk: dx - asin(theta)d(phi) = 0 -> 1. dy + acos(theta)d(phi) = 0 -> 2. are special cases of general linear diff-eqs of constraint of...

For the first question, I am only supposed to find the general solution of the differential equation. 1) dy/dt = -2ty + 4e^(-t^2) dy/dt + 2ty = 4e^(-t^2) Integrating factor = e^(Integral of 2t) = e^(t^2) Multiply both sides by IF: e^(t^2) * (dy/dt +2ty) = 4e^(t^2-t) e^(t^2)*dy/dt...

Homework Statement Solving this differential equation ty' + 2y = t^2 - t + 1 Homework Equations Its linear so i set it up in linear form y' + y(2/t) = t - 1 +1/t The Attempt at a Solution the integrating factor (u) = e ^ integral (ydt) = e^ integral (2dt/t)... Here's the...

Hello :smile: I've been stuck on this question for almost 3 hours now, and I still have no idea what to do. We haven't done a question like this in class, although we have done integration with partial fractions. Homework Statement Evaluate...

Homework Statement provided with data that dq = rho(r) *4phi*r^2*dr rho(r) = [Q*e^(-r/R) / 4phi R *r^2) I have to show that the charge q(r) enclosed in a sphere of radius r is q(r) = Q(1-e^(-r/R)) by using appropriate integral. how the integral should be? Homework Equations The...

Homework Statement Find the integral of (1-x)((2x-x^2)^.5) dx Homework Equations The Attempt at a Solution I am kind of hazy on U substitutions but I thought that was the right way to go here: let u=2x-x^2 du=2-2x (1/2) Integral of (u)^.5 du < i wasn't sure if I went wrong...

Homework Statement The ODE is (1+x)*dy/dx - xy = x+x^2 Homework Equations The method of solution is to be through the use of the integration factor. The Attempt at a Solution First, I divided each side by (1+x) to produce dy/dx - xy/(1+x) = x then factor out the x on...

Homework Statement I need to integrate (2x-5)/(x^2+5x+11) Homework Equations The Attempt at a Solution My problem is just finding a formula for an irreducable quadratic. I know if the denominator was x(x^2+1), I would use A/x+(Bx+C)/(x^2+1). I just don't know the formula in this...

During one lecture it was mentioned that equations of the form P(x,y)dx+Q(x,y)dy=0 always have at least one integrating factor. But the lecturer didn't know the proof, I've tried using Google but no luck. Anybody can show me the proof? Thanks a lot.

Homework Statement Show that the statement for Entropy dS = \int\frac{\delta Q}{T} is path independent Homework Equations The Attempt at a Solution I am trying to show this by stating that dS is an exact differential by stating how \delta Q is an inexact differential and by multiplying by...

I'm using a 3rd party physics engine to run rigid body physics. It just updates the bodies once every 16 ms or so. I'm trying to write an algorithm to predict where free-falling bodies will be in 2 seconds using standard physics equations. I'm having trouble with predicting angular velocity and...

Hi guys, Does anyone have any ideas about an analytical solution for the following integral? \int_{0}^{2\pi}J_{m}\left(z_{1}\cos\theta\right)J_{n}\left(z_{2}\sin\theta\right)d\theta J_{m}\left(\right) is a Bessel function of the first kind of order m. Thanks.

The question is If f(x) = 7x^3 + 8x^2 - x + 11, evaluate : a, Integral +1 - -1 f(x) dx b, Integral +1 - -1 f'(x) dx c, Integral +1 - -1 f''(x) dx For a, Just integrate each individual and then input the figures which gave me 1.75x^4 + (8x^3)/3 - 0.5x^2 + 11x Which when I input...