Integrating Definition and 940 Threads

Hello everyone! I was wondering.. if you could help me calculate some integrals: It's not for Homework or something, just my curiosity: \displaystyle{\int}\sqrt[3]{x^2-1} dx What would you suggest? I tried substitution, thou it seems to me useless. Are these integrals common in...

if f(x) = pi*xe^(-x^2) integrating this function if the lower boundary is 0 and the upper boundary is infinity is the answer pi*(2e-1). is this right?

I read, again in Spivak's Calculus on Manifolds, that the integral of 1-form over a 1-cube is equivalent to a line integral. And indeed, if I consider the 1-form w = Pdx + Qdy on R², and c a given 1-cube in R², I find that \int_c\omega = \int_0^1 F(c(t))\cdot c'(t)dt where F=(P,Q), which...

Homework Statement \text {Evaluate } \int^m_1 x^{3}ln{x}\,dx Homework Equations The Attempt at a Solution Integrating by parts, but not sure which term to substitute out...it's not turning out clean...argh I've done every other problem except for this one, can someone just...

Good old complex analysis. I'm trying to evaluate a line integral which looks like this \ointe (z + [1/z]) for |z| = 1 So I guess I'm dealing with a circle with a radius 1, so I've parameterised: z = eit I need to sub this into my formula of: \intc f(z)dz = \intf(z(t)) z'(t)dt (this is...

intergrating "e" I'm doing some intergration q's and I'm stuck on one which involves e [x^2 e^(x^3) ]dx I know to integrate you "add one to the power and divide by the new power.. would that make the solution ((x^3)/3) ((e^(x^4))/(x^4)? hope that makes a bit of sense..

Hello, I have a little project I'm playing with that involves calculating a series of forces and summing them to define the motion of an object (in this case, a walking pedestrian). The force equation is modeled on time-dependent vectors and scalars and is solved using Gear's...

Hi ok so te question is asking for me to fin the integrating factor of (y2x+y)dy + (x2y+2x)dy = 0 the only thing i know is that the integrating factor should be a function of xy Can some one pleas explain how to do this? Thank you.

Hi I am trying to integrate x \sqrt{1+x^2}dx by parts...but it seems to involve trigonometric functions - is it possible to solve this integral without using trig functions? Thx

Homework Statement Integrate. 1/ [e^x (1-e^(-2x))^1/2] Homework Equations integration by parts The Attempt at a Solution First I split up the integral so it would be (1/e^-x)[(1/(1-e^-2x)^1/2] Then I set u=e^-x, dv= (1-e^-2x)^-1/2 du= -e^-x For my v I got 2(1-e^-2x)^1/2 but I...

Homework Statement Am I doing this correctly? Is 2y^4dx +4xy^3dy exact or inexact? Homework Equations The Attempt at a Solution So if its exact, then M(x,y)dx = N(x,y)dy right? (Euler) But how can I take partial derivative of 2y^4 with respect to x, if there is no x to...

Plz explain me how can i integrate dw/rdr

Hello, I was looking at the differential equation (x^2 + 1) \frac{dy}{dx} + xy = 0. This solution to this equation has to be y = \frac{c}{\sqrt{x^2 +1}} So, when do we usually need to use the method of integrating factor? Can we solve all linear equations (1st order) using this method...

edit: Nevermind, I realized a way to find the answer after posting it. Though I still don't know about the thing involving the notes, can someone confirm if what I have written down as my teacher doing is true? Homework Statement note: I'll use this S as an integral symbol. S(ln...

-d[A]/dt = k[A] - Int( d[A]/[A]) = Int (k dt) - ( ln[A] + ln[A0] ) = kt ln[A] = -kt - ln[A0] Where am I wrong?

How do you set up an integral integrating two functions within a domain?? Homework Statement I have to integrate (2 + x + y) within the domain that is the area between 0 and 1 and (x+y<=1) I know how to integrate well, I think it's a double integral but I'm not really sure what the range...

An ACTUAL urgent post: Integrating exp() over certain range Hi, Simplified problem: Suppose I have two exponentials \[ e^{ - (x + a - b)} \forall x + a -b> 0 \] \[ e^{ - (x + b)} \forall x + b> 0 \] Then suppose I wanted to integrate: \[ \int\limits_{ - \infty }^\infty {e^{ - (x + b)}...

Homework Statement \int\sin(6\theta) d\theta Homework Equations The Attempt at a Solution \int6\cos6\theta Am I close?

Easier way of finding Integrating Factor for Exact Differential Equation?? Homework Statement ,find an integrating factor and then solve the following: [4(x3/y2)+(3/y)]dx + [3(x/y2)+4y]dy = 0 Homework Equations u(y)=y2 is a valid integrating factor that yields a solution...

Hello So I have a problem, which is to use integration by parts to integrate... \int^{1}_{0}(1-x) ln (1-x) dx The way I have been working is it to separate it out into just... \int^{1}_{0}ln (1-x) dx - \int^{1}_{0}x ln (1-x) dx and then integrating by parts on each of these...

Hello, I am trying to derive a function which describes the probability of two-photons interfering at a beamsplitter however I'm stuck on this particular integral. I need to solve: P(\tau,\delta\tau,\Delta)=\frac{1}{4}\int|\zeta_{1}(t+\tau)\zeta_{2}(t)-\zeta_{1}(t)\zeta_{2}(t+\tau)|^2dt The...

\int_{0}^{\pi/2}(cos(\theta)*exp(-2[\pi(1-cos(\theta))]^2)/k^2)/erf(2\pi/k) Where of course the error function erf is defined as: erf(x)=2/\pi\int_{0}^{x}exp(-t^2)dt Anyway... this is the problem I want to integrate. I am not looking for someone to post a solution. My question is...

I'm working on a project that requires me to numerically integrate the Planck spectral distribution. The object is to find the median wavelength, with exactly 50% of the radiance on either side. I'm using a standard composite Simpson rule method and I get good convergence with temps around...

Can anybody recommend a good site to bone up on differentiating and integrating ln and e functions?

Homework Statement \int\frac{\sqrt{x^{2}+1}}{x^{2}} dx Homework Equations The Attempt at a Solution I tried a Trig Substitution with x=tan(u) and ended up with \int (csc(u))^{2} * sec(u) du From here I am kind of stuck. I tried a few different integration by parts methods, but they got...

Homework Statement A solid "rough" of constant density (\delta =1) is bounded below by the surface z=4y^2,above by the plane z=4, and one the ends by the planes x=1 and x=-1. Find the center of mass...Homework Equations _{M}xy =\int\int\int z \delta dV Mass = \int\int\int\deltadV then to find...

Q: Given that G(x,y,z)=(6xz+x3, 3x2y+y2, 4x+2yz-3z2). Find F such that curl F = G. Solution: ... A particular solution is Fo=(-3x2yz-y2z, 2x2-3xz3-x3z) And then my textbook says that the general solution is F=Fo + grad f where f is an arbitrary C1 function...

Homework Statement Finding the area of a disc by integration of rings. Homework Equations A ring of radius r and thickness dr has an area of 2 \pi rdr. The Attempt at a Solution Why isn't it \pi (2rdr + (dr)^2)?

This integral came up while trying to find the potential of a uniformly charged rectangle. \int \log(\sqrt{a^2+x^2} + b) dx Integrator gives a pretty long expression involving inverse tangents so I'm not sure where to begin at all. I tried integrating by parts once, taking u to be the...

how do you integrate \frac{dy}{dx}=4x-2y. I don't know if this is right, but this is where I'm going with this: y'=4x-2y y'+2y=4x Solving homogeneous for complementary solution: y'+2y=0 Solving auxiliary equation: m+2=0 m=-2 Which gives y=c_{1}e^{-2x} y'=-2c_{1}e^{-2x}Now solving original...

Homework Statement \int tan^5(6x) sec^3(6x) dx Homework Equations The Attempt at a Solution first off I set u=6x to get 1/6\int tan^5(u) sec^3(u) dx then I used trig identities to put tangent in terms of secant and I came up with \int...

Homework Statement I would like to prove that {d \over {dx}} \sigma(x)=2\delta(x), where \sigma(x>0)=1 \sigma(x=0)=0 \sigma(x<0)=-1 Homework Equations The Attempt at a Solution I think that I need to show that \int_{-\infty}^{\infty}{d \over {dx}}...

[SOLVED] Integrating factors or separating the variables Homework Statement The following equation can be solved by intergrating factors or by separating the variables. \frac{dy}{dx} - \frac{y}{4x} = 0 with the initial condition of y(2)=3 Homework Equations The Attempt at a...

[SOLVED] Integrating Factor Diff Eqs Homework Statement g ' - g/t = t e^t I'm trying to solve this, but I seem to have run into a problem, according to my book the integrating factor is 1/t, however I believe that it is -t Homework Equations The Attempt at a Solution...

Homework Statement I need help integrating: mg/b(1 - e^(-bt/m) The Attempt at a Solution I came up with mgt/b - mg/b(-b/m * e^(-bt/m) It's been a while since calculus, can someone help me with this.

Homework Statement Use the substitution x=4sin(t) to evaluate the integral: S 1/[(16-x^2)^(3/2)] dxHomework Equations x = 4sin(t) The Attempt at a Solution x = 4sin(t) dx = 4cos(t) dt 4cos(t) = (16-x^2)^(1/2), i cube both sides to get (4cos(t))^3 = (16-x^2)^(3/2), then plug in dx and...

I am trying to evaluate the following integral. \int_{-\infty}^{\infty}{\delta(2t-3)\sin(\pi t) dt} where delta represents the Dirac delta function. I am told that the answer is -1. However, when I evaluate it in MATLAB and Maple 11, I get an answer of -1/2. What is the correct way...

I was trying my hand at integrals with 2 variables... So.. my first excercise was to find out the surface area of a sphere. So, the co-ordinate system is something like this: i] The whole co-ordinate system is mapped on the surface of a sphere. ii] The x-axis of the sphere is like the equator...

Homework Statement Not real good with the easy text stuff yet so ill give it a shot. definite integral of (1/(1+t^2))dt from 0 to x^2 then find the interval for which the curve is concave upward. I totally forgot how to integrate problems like this. It is some sort of substitution I...

how do i integrate 1/(x^2 +4)? please help

Homework Statement Integrate the following \int\sqrt{1-sin2x} dx Homework Equations sin2x=2cosxsinx cos2x= cos^2 (x) -sin^2 (x) The Attempt at a Solution I've rearranged the integral so its 1-sin2x/\sqrt{1-sin2x} but other than that I've just been randomly trying stuff. Any hints...

Integrate sqrt(1 +a^2*x^2) dx Thanks

Hi everyone. I was curious how I could integrate a matrix. Is it just as simple as separately integrating each of the entities of the matrix, or is it more complex than that?

[SOLVED] Integrating substitution problem? Homework Statement Sorry to hijack this thread sort of (as a similar named one already exists), but the title is aptly suited to my question. I have integral to integrete and I don't really know how to do it tbh. . . s=\int{\sqrt{2+(3t)^2}dt...

the intergral of 1/3x either equals 1/3 ln 3x or 1/3 ln x - i don't know which one is correct though because can't you take the 1/3 out of the intergral and then you get 1/3 ln x - so confused - i should really know this...

Hi, I'm trying to integrate an expression I derived from multiplying the Fourier transform of two Lorentzians together. The expression is \int^{\infty}_{-\infty}{dt.e^{-|t + \tau +a| - |t-a|} How do you go about solving this? I tried splitting it up but you have two different values of t...

I am trying to integrate (sin(x))/x It's an indefinite integral I can't think of any tricks to work this out

Homework Statement Using the macluarin's expansion for sinx show that \int sinx dx=-cosx+cHomework Equations sinx=\sum_{n=0} ^\infty \frac{(-1)^nx^{2n+1}}{(2n+1)!} The Attempt at a Solution Well I can easily write out some of the series and just show that it is equal to -cosx but if I...

Homework Statement A. (1-sin^2x)/(cos^2x) dx Upper Limit = pi/4 Lower Limit = 0 B. (x-2)/(sqrt x) dx Upper Limit = 4 Lower Limit = 1 Homework Equations The Attempt at a Solution A. I am having trouble with this one. B. (x - 2)/(x^1/2) = (x^1/2 - 2x^-1/2) = 2/3x^3/2 -...

Hi, I am having some difficulties integrating the following expression.. \int\int\left(\frac{k}{\pi}\right)^2 \frac{1}{k^2+\omega'^2}\frac{1}{k^2+\omega^2}e^{-i\omega'\tau}e^{i\omega\tau}d\omega d\omega' I've tried by part but it doesn't look like it's going to give me the right answer...