Integrate Definition and 642 Threads

Homework Statement Integrate f(z) = Re(z) = \frac{z+\bar{z}}{2} along the contour of the square {z = x + iy | |x| ≤ 1, |y| ≤ 1} with counterclockwise rotation. Homework Equations Cj: φj(t) = z0 + (z1 - z0)t C1: 1 -i + 2it C2: 1 +i - 2t C3: -1 +i - 2it C4: -1 -i + 2t The Attempt at a...

Homework Statement My solution has two terms divided by a which is in error. I am a volunteer math coach to some junior college students and can't find my error in the problem. Its been a while since I earned my masters in electrical engineering. The issue is the presencce of the variable...

If k is a constant, I know \frac{d}{dx} \ln(x) = \frac{1}{x} \frac{d}{dx} \ln(kx) = \frac{k}{kx} = \frac{1}{x} However, what about \int\frac{1}{x}. I've been taught to use \int\frac{1}{x} = \ln(x), but wouldn't \int\frac{1}{x} = \ln(kx) work as well. And if this is true, there are an...

The question is attached . N/A I tried to integrate it using cos^2x=t But it didn't work . The numerator is killing me. Euler's equations are not applicable here . Therefore they don't work here . Thus how to solve it ?

Homework Statement Integrate: (e^(2t))(25sint+20cost)dt Homework Equations Integration by parts twice The Attempt at a Solution I don't know what to set for u and v. I ended up wolfram alpha it but I want to know how to get there. The solution is: e^(2t)(14sint+3cost)=C

Homework Statement How to integrate dv/dt=g-kv/m? Homework Equations This is ODE. The Attempt at a Solution dv/(g-(kv/m))=dt Now what? I don't know how to integrate the left side.

Homework Statement Integrate x*sqrt(1-x^2)+(1-x^2)/2 dx from 0 to 1. Homework Equations None. The Attempt at a Solution How do I simplify this and find the integral of this?

Homework Statement How to integrate the double integral cos(x+y) dy dx from 0 to pi and from 0 to pi again. Homework Equations The answer is -4. The Attempt at a Solution Here's the work: u=x+y du=dy cos(u)du=sin(x+y) integral of [sin(x+y)] evaluate from 0 to pi dx from 0 to pi integral of...

Homework Statement http://s23.postimg.org/wsj9e91wb/IMG_1334.jpg[/B] photo of the problem g(x)=∫ƒ(t) dt from -5 to x ƒ(t) = (0 if x < -5 5 if -5≤x<-1 -3 if -1≤≤x<3 0 if x≥3) (a) g(-8) = 0 (b) g(-4) = 5 (c) g(0) = ? (d) g(4) = ? Homework Equations ∫ƒ(x) from...

Homework Statement How to solve for Q in dQ/dt=2-0.1Q? Homework Equations None. The Attempt at a Solution dQ/(2-0.1Q)=dt Now what?

So v' is the one to be integrated and v is the answer, why is it not -xe^-x - e^-x ? :confused: Thank you very much!

Homework Statement ##\int \frac{d}{dx} (x^2y)## ? Explain please and give me some hints. Homework EquationsThe Attempt at a Solution

Question: A single conservative force acts on a 5.00-kg particle. The equation Fx = (2x + 4) N, where x is in meters, describes this force. As the particle moves along the x-axis from x = 1.00 m to x = 5.00 m, calculate (a) the work done by this force. Work = Force * Distance. (2*(5-1) +4) =...

Homework Statement FIRST ##\int x^2 \ln x \ dx## SECOND ##\int \frac{(x+1)^2}{x}dx## THIRD ##\int \frac{x-2}{x+3}dx## Homework Equations N/A The Attempt at a Solution I tried using the integration by part method but it doesn't work. For the FIRST problem: Setting ##u=x^2## or ##u=\ln x##...

I don't understand the question: "First make a substitution and then use integration by parts to evaluate the integral" \int sin \sqrt{x} dx What does it have in mind by "substitution"?

Homework Statement Integrate e^(ax+by)(a*cos(xy)-y*sin(xy)) with respect to x. Homework Equations None. The Attempt at a Solution The answer is (cos(xy))(e^(ax+by)). I know that I need to treat y as a constant since I'm integrating it with respect to x but I don't know how to integrate this...

Homework Statement How to integrate dz/(z^2+2z/x)? Homework Equations None. The Attempt at a Solution I did partial fractions but it doesn't seem to work. A/z+B/(z+2/x)=1

Hello, I'm hoping somebody can give me some insight on how to solve this problem. This was a solid mechanics exam question and I wasn't able to finish it because I'm rather weak in math. 1. Homework Statement Homework Equations Recall divergence theorem for part ii. ∫div(V)dA = ∫V⋅ndS where...

Homework Statement Let f(x1, x2, x3) = e-(x1+x2+x3), 0<x1,2,3<infinity, zero elsewhere be a joint pdf of X1, X2, X3. The variables are all independent to each other Compute P(X1< X2< X3|X3<1 ) Homework Equations P(X1< X2< X3|X3<1 ) The Attempt at a Solution P(X1< X2< X3|X3<1 )=P(X1< X2< X3<1...

i only can integrate a k-form in a n-dimensional manifold, if k=n right?

Homework Statement I need to integrate x/sqrt(a^2+b^2-2abx) with respect to x. The Attempt at a Solution This follows from a substitution of the form x=cost in a textbook I'm reading - they jump to the solution straight from the above and I have no idea how to go about it - any hints will...

Hello! I'm having some trouble determining, when trying to find the area between two curves, when to integrate with respect to y or respect to x, given two equations only? Thanks!

Integrate[f[qs] DiracDelta'[qs (1 - 1/x)], {qs, -\[Infinity], \[Infinity]}, Assumptions -> 0 < x < 1] Integrate[f[qs] DiracDelta'[qs - qs/x], {qs, -\[Infinity], \[Infinity]}, Assumptions -> 0 < x < 1] This is on Mathematica 8 for windows. The results differ by a sign. They are effective...

Homework Statement How to integrate∫√(2+2sinθ) Homework Equations Making use of (2+2sinΘ)(2-sinΘ)=4-4sinΘ^2 The Attempt at a Solution Multiply and dividing the integrand by √2-2sinΘ

Hello, For a practical I have to know the work done by drag force, but drag force which is bv2 is not constant over the path, how can this be done, or should I just add every tiny bit of work, supposing Fd is constant over that tiny path. Thanks for the help!

∫x(x^{2}+1.44)^{-1/2}(dx)The only technique of integration I know of is to recognize the antiderivative (which I can do for this one but) I'm tired of being limited by antiderivatives.I was wondering how would you go about solving this?

Homework Statement The c.d.f. of a random variable X is given by the following formula F(x) = 1 - e-x2 x≥0 Find M(t). Moment generating function. The Attempt at a Solution I've found the pdf as f(x) = F'(x) = 2xe-x2 x≥0 To determine M(t) I need to do the following...

∫sin(x^3) dx I have absolutely no clue on what to deal with the x^3 part. All I can think of is this: ∫sin(ax) dx = -1/a cos(ax) + C

I would like to know how do we solve d2x/dt2 = k' where k' is a constant i.e the task is to find x as a function of time ? One way to approach this is to rewrite it as vdv/dx = k' where v=dx/dt and first find find v as a function of x and then rewrite v as dx/dt and then find x as a function...

Homework Statement ∫tan3x dx 2. The attempt at a solution ∫tan x + ∫tan2x ∫tan x (sec2x - 1) dx ∫(tan x (sec2x - tan x) dx ∫tan x sec2x dx - ∫tan x dx u = sec x du = sec x tan x dx ∫tan x sec x sec x - ∫tan x dx Now I'm stuck.. ∫ du * u - ∫ tan x dx ?

i'm trying to integrate this: $$W=\frac{ε}{2}\int{\vec{∇}\cdot\vec{E})Vdτ}$$ where ε is a constant, E= -∇V, τ is a volume element how do i end up with the following via integration by parts? $$W=\frac{ε}{2}[-\int{\vec{E}\cdot(\vec{∇}V)dτ}+\oint{V\vec{E}\cdot d\vec{a}}$$] where the vector a...

I'm trying to derive Saha's equation, and I've come up against this definite integral, which I can't seem to find anywhere and may not even be doable; I'm not sure. \begin{equation} \int\limits_0^\infty \frac{x^{2}}{e^{x}+1}dx \end{equation} Can anyone help? Thanks!

Homework Statement Calculate ##\int _Kz^2exp(\frac{2}{z})dz## where ##K## is unit circle.Homework Equations The Attempt at a Solution Hmmm, I am having some troubles here. Here is how I tried: In general ##\int _\gamma f(z)dz=2\pi i\sum_{k=1}^{n}I(\gamma,a_k)Res(f,a_k)## where in my case...

I'm trying to integrate the function Exp[-I*t*x - t^2/2] from -infinity to infinity using NIntegrate in Mathematica; the value that I get is accurate when x is small, but as x gets larger, the output from NIntegrate does not match the value I get when I use Integrate -- it gets less and less...

Homework Statement Numerically integrate and plot the response of an underdamped system determined by m= 100 kg, k= 20,000 N/m, and c = 200 kg/s, subject to the initial conditions of x0 = 0.01 m and v0 = 0.1 m/s, and the applied force F(t)=150cos(5t). Then plot the exact response. Homework...

Hey! :o I have the following exercise: Integrate the function $f=x+ \sqrt{y} -z^2$ at the path from $(0,0,0)$ to$(1,1,1)$ that consists of the curves $C_1:r(t)=t \hat{ \imath}+t^2\hat{ \jmath}, 0 \leq t \leq 1$ and $C_2: r(t)=\hat{ \imath}+\hat{ \jmath}+t \hat{k}, 0\leq t \leq1$.My solution is...

https://www.physicsforums.com/attachments/67272 I need some help, thank you:-)

Here is the code, I am using Mathematica 7 with no packages installed at the moment. $Assumptions = 0 < u <= 19/80 && I10 \[Element] Reals; FXN = Sqrt[(u - 15/16)^2 - 2/5 (u + 17/16) + 1/25] (I10 (u^2) - 1/u); PA = Integrate[FXN /. {I10 -> 1/2 Log[1/2]}, u]; PB = Integrate[FXN, u] /...

Homework Statement A flat ring of inner radius R1 and outer radius R2 carries a uniform surface charge density σ. Determine the electric potential at points along the axis (the x axis). [Hint: Try substituting variables.] Homework Equations V = (kQ)/r The Attempt at a Solution...

Here's the problem I was given: Find the area of the surface generated by revolving the curve $$x=\frac{e^y + e^{-y} }{2}$$ from 0 $$\leq$$ y $$\leq$$ ln(2) about the y-axis. I tried the normal route first... g(y) = x = $$\frac{1}{2} (e^y + e^{-y})$$ g'(y) = dx/dy = $$\frac{1}{2} (e^y -...

Homework Statement Find the area of the surface generated by revolving the curve x=\frac{e^y + e^{-y} }{2} from 0 \leq y \leq ln(2) about the y-axis. The Attempt at a Solution I tried the normal route first... g(y) = x = \frac{1}{2} (e^y + e^{-y}) g'(y) = dx/dy = \frac{1}{2}...

Homework Statement I am suppost to integrate e^x^2 from 0 to 1 and such, I using Maclaurins rule, I got e^x=1+x/1!+x^2/2!+...+x^n/n!+e^(öx)*x^n+1/(n+1)!, 0<ö<1. But when I put in x^2 instead of x, I end up with a legit thing except e^(öx^2)x^n+1/(n+1)! and this is giving me e^x^2 again!

I'm wondering how to integrate something of the form 2^x * e^x. I tried using integration by parts, ∫u dv = v*u - ∫v du. The problem is no matter which term I choose to integrate and which to differentiate, the final solution still has an integral with a product of terms in the form (2^x)...

Homework Statement This function of one variable need to be integrated: f(x)=1/(9+7*(sinx)^2) from x=0 to x=pi, without help with calculators or computer algebra software. Homework Equations Have no idea. The Attempt at a Solution Have no idea. I don't have any idea how to start. Please...

Homework Statement Integrate sqrt(1+4x^2) limits x = 0 to x = 1 Homework Equations The Attempt at a Solution let 2x = sinhu I = 0.5 ∫ (coshu)^2du limits u = 0 u = sinh^-1(2) 0.5 ∫ (e^2u +e^-2u +2)/4 du 0.5 [(e^2u)/8 -(e^-2u)/8 +2u] I = 2.56 which is wrong :( why is it wrong? please help!

Homework Statement $$xy'' = y' + (y')^{3}$$Homework Equations $$ y'' = p' = \frac{dp}{dx}$$ $$ y' = p$$ The Attempt at a Solution $$xy'' = y' + (y')^{3}$$ $$ x*\frac{dp}{dx} = p + p^{3} $$ $$ \frac{dx}{x} = \frac{dp}{p+p^3} $$ $$ ln x + C = ∫\frac{dp}{p(1+p^2)} $$ $$ u = p^{2} $$ $$du = 2p...

how would I integrate -y'/(y-3)y??

Homework Statement I have to find the ratio of RB/RA where R is electrical resistance. Both objects A and B have circular cross section and length L, and are made of the same material. A has radius r0. B has radius r0/2 at the bottom and increases linearly to 2r0. Homework Equations...

For example, let's say there was an block infinitely long in the x and y direction and in the z direction bounded by positive and negative a. I am trying to find the charge of a imaginary partition infinitely long in the x and y direction and in the z direction bounded by positive and...

I learned how to integrate it using the complex plane and semi circle contours but I was wondering if there is a way using Fourier transforms. I know that the Fourier transform of the rectangle wave form is the sinc function so I was thinking maybe i could do an inverse Fourier on sinc x and get...