Integrating Definition and 971 Threads

I have been looking for problems to work out for practice and came across one I have no idea how to even start about. Say a box is dropped from a plane, with a parachute attached to it. If we are given two equations for velocity in terms of time, such as Vx(t)=Vo cos(θ) e^(-pt) and...

Homework Statement Integrating X^3/((e^x)-1), where we integrate from -infinity to infinity The Attempt at a Solution We thought about it, and we're not entirely sure if integration by parts is applicable here. Is there a table with this function perhaps?

Homework Statement integrating a circle ,, my main question is that, can we integrate it by contour integration technique ? and if yes ,, would you please show me how :) or just give me a hint :D Thanks is advance :-) Homework Equations y^2 + x^2 = a^2 where a= r suppose...

Homework Statement Specifically what i don't understand is a situation where you can't get the equation in the standard form of y' + p(x)y = q(x) the integrating factor is e^integ p(x), but what if y is part of a sin or cos, as in this equation: (x+2)sin y dx + xcos y dy = 0 if i...

Homework Statement Solve (x+2)sin y dx + xcos y dy = 0 by finding integrating factor mu(x) Homework Equations i put equation in standard form to get integrating factor dy/dx + (x+2)sin y / x cos y = 0 but don't i need to get the y out of the sin and cos somehow? so that...

Homework Statement verify that mu= 1/(y^4) is an integrating factor of: (3x^2 - y^2)dy/dx - 2xy = 0 and use it to solve the equation. Homework Equations (3x^2 - y^2)dy/dx - 2xy = 0 first i want equation in standard form right? dy/dx - 2xy / (3x^2 - y^2) = 0 then mu =...

question: Consider the gaussian distribution: p(x) = Ae^(-\lambda (x-a)^2) (a) use the equation, 1={\int_{-\infty}^{\infty}} p(x)dx (b) find <x>, <x^2> and \sigma ------------------------------------------------------ a) if i take (x-a) to be u, 1=\int_{-\infty}^\infty...

Homework Statement The question asks that you prove that \int\frac{sin^{2}x}{x^2}dx = \pi / 2 The integral is from zero to infinity, but I don't know how to add those in latex. Homework Equations Use a contour integral to get around the pole at z = 0. The problem is, I'm really really foggy...

Homework Statement my integrating factor for the DE ty' + (t+1)y = t is mu(x) = e^integ (1+(1/t)) = e^(t + ln|t| + c) so does this simplify to this...or not? = e^t + t + c so that DE becomes: ((e^t) + t))y = (e^t) + t) and then after integrating... ((e^t) + t))y = e^t +...

Orthonormal basis \big(\frac{1}{\sqrt{2}}, cos(2x)\big) \pi \int_{-\pi}^{\pi} sin^4(x)dx=\frac{3\pi}{4} Solve the integral without integrating. sin^4(x)=\big[\frac{1-cos(2x)}{2}\big]^2=\frac{1}{4} - \frac{2cos(2x)}{4} + \frac{cos^2(2x)}{4} I know I could rewrite cos^2(2x) but then I...

Homework Statement Solve: (1-\frac{x}{y})dx + (2xy + \frac{x}{y} + \frac{x^2}{y^2})dy = 0 The Attempt at a Solution No idea what strategy to use here. Tried using an integrating factor, but no success. A lot of x/y in here makes me think I need to use a substitution, but there's also...

Homework Statement solve the following initial condition problem x (d/dx) y(x) + 4xy(x) = -8-y(x) y(4)=-6 Homework Equations The Attempt at a Solution first i rearranged xy'+y+4xy=-8 xy'+y(1+4x)=-8 y'+y(1/x+4)=-8/x integrating factor:e^\int(1/x+4) e^(lnx+4x) x+e^4x multiplying...

y' + y = e^x ; y(0) = 1 1st, i calculate the integrating factor... u(x) = e^x times the integrating factor with DE... y'e^x + ye^x = e^2x dy/dx e^x + ye^x = e^2x d/dx ye^x = e^2x ye^x = ∫ e^2x dx ...= 1/2 e^2x + C y = 1/2 e^x + C the problem here, i didn't get the...

Question: (1 - x - z)dx + dz = 0 let M = (1 - x - z) ; N = 1 dM/dz = -x ; dN/dx = 0 hence, not exact. integrating factor... 1/N[ dM/dz - dN/dx ] = 1[-x] .......= -x e^∫-x dx = e ^ [(-x^2)/2] times integrating factor with DE.. {e ^ [(-x^2)/2] -x e ^ [(-x^2)/2] - z e ^...

y dx + x ln x dy = 0 ; x > 0 my integrating factor is x.. so.. multiply with DE, xy dx + x^2 ln x dy = 0 let M = xy ; N = x^2 ln x dM/dy = x ; dN/dx = x + 2x ln x the problem is.. i didn't get the exact equation after multiply the integrating factor.. I've double...

Homework Statement Show that given function μ is an integrating factor and solve the differential equation.. y^2 dx + (1 + xy) dy = 0 ; μ(x) = e^xy The Attempt at a Solution let M = y^2 N = (1 + xy) dM/dy = 2y dN/dx = y hence, not exact equation. times μ(x) = e^xy to the...

Hey guys working on a problem for an assignment but my algebra is weak regrettably and I need some assistance. Note:: I left the x and dx out for clarity. Homework Statement int csc/cot2 The Attempt at a Solution int csc x/cot2x dx= int csc/cos2/sin2 = int cscsin2/cos2 = int...

Hello, Just wondering if someone can help me make sense of something. I realize it's probably a simple problem, but my math skills aren't the best and I can't see through it. I'm trying to end up with this kinematic equation: X= Xo + Vo(t-to) + 1/2(a)(t-to)^2 And to do this the...

hello, I'm new to the forums. Can someone help me with integrating kinematics problems? For example velocity= Be^(-rt), where B= 3.00 m/s and r=0.500 s^-1. i don't understand how the integral's unit becomes m (since the integral of velocity is displacement). someone help me! thanks

Homework Statement \int dx/(e^{x}\sqrt{1-e^{-2x}}) Homework Equations The Attempt at a Solution I have absolutely no idea of how to start the problem, any help is greatly appreciated! thanks!

When we integrate a function f(t) with respect to t, we are finding the area under the curve f. Intuitively, this is very clear. What is the intuition behind integrating a function with respect to another function? ex. \int f(t)dg where g is itself a function of t?

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...

(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| = Integral(G(xy)) by...

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 the general solution for this differential equation. dy −2x^2 + y^2 + x dx = x yHomework Equations The Attempt at a Solution dy/dx = (−2x^2 + y^2 + x) / (x y) let y^2 = v dy/dx = v + x dv/dx v + x (dv/dx) = (-2x^2 + v^2 x^2 + x ) / v x^2 => x (dv/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...