Integrating Definition and 940 Threads

Can someone help solve these two equations: 1. T[Cos(t)] = ∫[Sin(t-x)Cos(t)]dx the limits are from 0 to 2pi 2. T[Sin(t)]=∫[Sin(t-x)Sin(t)]dx; the limits are from 0 to 2pi Thanks

Hi I'm trying to compute the following integral (in LaTeX notation; * denotes multiplication) \int_0^{2\pi} exp (k_1 * cos (t + k_2)) d t with k_1 and k_2 being known constants. Furthermore k_2 is between 0 and 2 pi. From Wikipedia [1] I get the following formula \int_0^{2\pi}...

I've been trying to evaluate an integral for the last few days now and it really has me stumped. I was hoping that maybe someone here would be able to help me out. So the function, cov(x,x'), is fairly basic. It's called a squared exponential covariance function and it evaluates the covariance...

I'm in an electronics course, and the book derives an equation for the current-voltage characteristics of an NMOS transistor. In doing so, it integrate this: \int_{0}^{V_{DS}}V(X)\, dV(X)=\frac{V_{DS}^2}{2}I can see that integrating a function F(X) with respect to F(X) turns out to be the same...

from -2 to 2, integral Ln(√(4-y^2)+2)dy, how to integral that?

Homework Statement A spherical distribution of charge is characterized by a constant charge density \rho for r<= R. For radii greater than R, the charge density is zero. Find the potential \varphi (r) by integrating Poisson's equation. Homework Equations...

Homework Statement So I'm trying to find the integral of P = 2xyz^2 along the curve c which is defined by: x=t^2 y=2t z=t^3 t goes from 0 to 1 So the q says that it is the integral of P dr along c Homework Equations The Attempt at a Solution So I know that this...

([SIZE="2"]Moderator's note: thread moved from "Differential Equations") M(x,y) + N(x,y)(dy/dx) = 0 f'(xy) = G(xy)f(xy) where G(xy) = (Nx - My)/(xM - yN) Replace xy with a single variable to obtain a simple 1st order differential equation and find f(xy). I got to: ln|f| =...

How would you integrate something like xe(x^2) by using a substitution like u=x^2

http://www.freeimagehosting.net/image.php?9722bd5444.png Link: http://www.freeimagehosting.net/image.php?9722bd5444.png" I've tried to used integration by parts and u substitution and I've also tried just multiplying the fraction by the denominator (6-x)^(1/2) but I am still confused at...

Integrating factor! As promised I'm back with integrating factor differential equation.(x^2 + 1)dy/dx -2xy = 2x(x^2+1) y(0)=1 First put into standard from by dividing thru by (x^2 +1 )dy/dx -2xy/(x^2 + 1) = 2x Integrating factor is given by exp( integral of -2x(x^2 + 1))...

Hey guys, I'm studying for a test in calc 3 tomorrow and have run into a problem. On the practice test we have a problem "Find the length of the curve: r=theta^2, 0≤theta≤pi/2" I know the length of a curve in polar coordinates is int(sqrt(r^2 + (dr/dtheta)^2))dtheta...but when I get to where...

Homework Statement total charge Q = 200[nC] is spread along a line from x=−100[mm] to x=+100[mm] . a) write the dV caused by each dQ=λ dx . b) integrate along the line of charge ; write V as a function of y . c) take the derivative with y , to obtain that component of...

Homework Statement http://img37.imageshack.us/img37/1237/63391287.jpg Homework Equations $\displaystyle \Large \int udv$ = uv - $\displaystyle \Large \int vdu$The Attempt at a Solution can i take this 3 out of the integral as well and make it 3/8 *$\displaystyle \Large \int _0^8 sqrt(64 +...

Homework Statement I need to solve the integral \int \frac{dx}{\sin{x} |\sin{x}|}. Homework Equations - The Attempt at a Solution I know it's possible, the solution is -\frac{\cos{x} |\sin{x}|}{\sin^2{x}}, and I probably need to write the absolute as the square root of a...

Homework Statement Hi, can anyone help me solve a differential equation for the logistic growth model? Homework Equations It reads: M'(t) = M(S-M) + I, where M(t) represents the growth of a biomass. "I" represents immigration (in a coral reef) and there is no breeding...

Homework Statement \int\frac{xe^{2x}}{(2x+1)^2}dx where "e" is the natural number Homework Equations (none) The Attempt at a Solution I tried many ways to solve this problem, but to no avail. the hint on the book said to use substitution and make u=xe^{2x} and du=2xe^{2x}+e^{2x}dx...

Homework Statement Find all solutions of the equation: y' = (2y)/(t.logt) = 1/t, t > 0 Homework Equations Integrating factor I = exp(\intp(x)dx) where y' + p(x)y = q(x) The Attempt at a Solution Hi everyone, here's what I've done so far: Let p(t) = -2/(t.logt) I =...

Homework Statement An Integral : \int \frac{1}{x^n(1+x^n)^{1/n}} \;\mathrm{d}x} Homework Equations The Standard integrals. The Attempt at a Solution I'm aware that integrals like this become very easy after a clever substitution...but maybe I'm not that clever...

Homework Statement \int delxA dv = -\oint Axds where A is a vector field Left hand side is integral over volume. Right hand side is integral over closed surface. Homework Equations The Attempt at a Solution Can't understand what Axds means.

Homework Statement Integral [x] - 2[x/2] dx limits are 0 to 2 I am using [] to represent the floor function. Homework Equations The Attempt at a Solution Of course normal integration gives x^2/2 - x^2/2 which gives 0 for all cases, So is it right to assume a floor function...

\int_0^{\pi} \frac{x}{1+\sin(x)\cos(x)} dx

I guess people who know can help. I know that the final formula should look like this: (OMEGA) = 4tan^(-1) [(e)/n(1+e^2+n^2)^(0.5)] , where e=W/L, n=2z/L I started with D(omega) = dAcos(theta) p^2 cos (theta) = z/p then i did a bunch of...

whenever i see that integrating factor for solving a linear differential equation with eint. p(x) dx and then multiplied out in the equation, there seems to be no constant. i tried solving an equation with it the other day, and got an incorrect solution because of it (i think. at least i got a...

Homework Statement A) Find the volume of a truncated pyramid with a regular hexagonal base. perimeter of bottom = 1.2 km perimeter of top = 480 m height = 200m B) If density = 1500 kg/m^3 how much work was done in construction? Homework Equations The Attempt at a Solution I...

Homework Statement Express f(x,y) = 1/sqrt(x^2 + y^2) . (y/sqrt(x^2 + y^2)) .exp(-2sqrt(x^2 + y^2)) in terms of polar coordinates \rho and \varphi then evaluate the integral over a circle of radius 1, centered at the origin. Homework Equations x = \rhocos\varphi y =...

Hello, First of all, I am not trying to "spam" subforums. I found out that my thread shouldn't be posted under homework. Anyways, here it is. Integration Let say there's a polynomial, 5x+6 and you want to integrate from 0 to 3 respect to x, how do you input in MATLAB? (I guess you can't...

Homework Statement Integrate exp(-3(sqrt(x**2 + z**2 + y**2))) over infinite space [-inf, inf] on xyz Well transforming to spherical coordinates leaves me with the equation at 3.attempts at a..() but here is my problem, how can you equate an integral over an infinite space to a spherical...

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 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?