Integrating Definition and 971 Threads

Homework Statement Hi. I ve got a problem, where I have to show torque by integrating the weight of the rod over the whole it's length. Homework Equations [/B] Result, what I am suppose to get is: ## \tau_{rod} = \frac{mgb}2 ##The Attempt at a Solution [/B] When I try to integrate, I am...

Homework Statement (e^(ikx)/(x^2+a^2))dx (-infinity, +infinitiy) Isn't this function odd so it should be zero?Homework EquationsThe Attempt at a Solution I know how to complete the entire problem but I'm having troubles integrating this. I'm looking for someone to reference ( a website or an...

Homework Statement acceleratin as function of time ##a(t)= 2t+1## we know that v(0)=0 and s(0)=0 find v(t) find v(5) find s(t) find s(3) and I was thinking about also what happens when t is negative number, is it possible to find also v(-2)? what about s(-3)? Homework Equations integration...

Hi PF! I am trying to integrate functions over an infinite domain. One example is $$\int_0^\infty \frac{e^{-x}}{\sqrt{x}}\,dx$$ I know the substitution ##u = \sqrt{x}## reduces this problem to integrating ##\exp(-x^2)##, but if I want to integrate the function as is, how would I do this? I've...

Hi all, just a quick question: I'm trying to integrate this function in two different ways and I'm getting a different answer each way, can someone please quickly tell me where I'm going wrong? I've read through it for a couple hours and can't pick up the mistake. ##\int _{ }^{...

I came across this step in a derivation:$$m\ddot{r}=\frac{L^2}{mr^3} -V'(r)$$ Multiplying by ##\dot{r}## and integrating with respect to t to get $$\frac{1}{2}m\dot{r}^2+\frac{L^2}{2mr^2}+V(r) = C$$ I am not very clear about how the 1st term came to this. Can some one gives a pointer?

Homework Statement Find an integrating factor of the form ##x^Ay^B## and solve the equation. ##(2y^2-6xy)dx+(3xy-4x^2)dy=0## Homework Equations ##M=2y^2-6xy## ##N=3xy-4x^2## ##IF = exp(\int \frac{M_y-N_x}{N}\,dx)## or ##IF = exp(\int \frac{N_x-M_y}{M}\,dy)## The Attempt at a Solution [/B]...

Say we have two functions; ##f\left(x\right)=\frac{1}{e^x-1}## and ##g\left(x\right)=\ln \left(\frac{1}{x}+1\right)##. Let us find the limit of both functions as x approaches infinity; ##\lim_{x \rightarrow \infty} {f(x)} = \frac{1}{e^\infty-1} = \frac{1}{\infty} = 0## Therefore as ##x...

Homework Statement I have a 2D integral that contains a delta function: ##\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\exp{-((x_2-x_1)^2)+(a x_2^2+b x_1^2-c x_2+d x_1+e))}\delta(p x_1^2-q x_2^2) dx_1 dx_2##, where ##x_1## and ##x_2## are variables, and a,b,c,d,e,p and q are some real...

To find the surface area of a hemisphere of radius ##R##, we can do so by summing up rings of height ##Rd\theta## (arc length) and radius ##r=Rcos(\theta)##. So the surface area is then ##S=\int_0^{\frac{\pi}{2}}2\pi (Rcos(\theta))Rd\theta=2\pi R^2\int_0^{\frac{\pi}{2}}cos(\theta)d\theta=2\pi...

I have a function of force with respect to a certain angle, θ. I also have the angle of the force, Ψ, with respect to the same angle. Plug in θ, get the force and Ψ. This function is determined by a table of data: F(θ) and Ψ(θ) This force is acted upon a beam at a distance L from a pivot at one...

I'm looking at different ways to express the derivative a curve, like circular and tangent/normal components. Is there no such way that let's you express a vector integral in terms of information from the vector you want to integrate?

I am working my way through a textbook, and whenever this equation is solved (integrated), the answer is given as: u = f(x) + f(y) I don't understand it. If I integrate it once (with respect to y, say), then I obtain: ∂u/∂x = f(x) -----eq.1 If I integrate again (this time with respect to...

Homework Statement ##cos t \frac{dv}{dt} + (sin t) t = \frac{GM}{b^2 }\sin^3 t ## Homework Equations above The Attempt at a Solution im pretty stuck to be honest. It almost looks like a product rule on the LHS but it has the wrong sign, RHS I've tried writing ##sin^3 t## as ##(1-cos^2t)\sin...

Hi (1/sqrt(4t²+1), 2t/sqrt(4t²+1)) gives a unit tangent to the curve y=x^2 at point (t,t^2). Viewing the vector as velocity, shouldn't I be able to integrate it and get a parameterization for y=x^2?

I am studying a paper and a math step like this was used: dt'=(1+\frac{h}{2}sin^2(\theta))dr \\ \int^{t1}_t dt'=\int^d_0 (1+\frac{h}{2}sin^2(\theta))dr \\ where\\ h=h(t-\frac{r}{c}-\frac{r}{c}cos(\theta)) This seems wrong because it seems to me that you're not doing the same thing to both...

x2 + y + y2dx - x dy = 0 Integrating factor, I(x,y) = -1 / (x2 + y2) How to find the integrating factor ?Why I cannot use below method to solve the ode ? (1/N)(My - Nx) = g(x) , I(x,y)=exp( ∫ g(x) dx) OR (1/M)(My - Nx) = h(y) , I(x,y)=exp( -∫ h(y) dy)

Hello, I was just wondering about the method for integrating Friedmann equation for k=1 and w=1/3 ∫(8πρ/a^(2)-1)^-1/2thank you

\begin{align*}\displaystyle I_{7}&=\int_{0}^{\pi/8}\frac{\sec^2(2x)}{2+\tan\left({2x}\right)} \\ &= \end{align*} not sure of the u substitution here... if $u=tan(2x)$ then $du=2sec^2(2x)$ but stuck with 2 in the denominator after subst

This isn't exactly homework or coursework, it is a past paper question that I cannot find a solution to (my university doesn't like releasing answers for some reason unknown to me). The question is attached as an image (edit: the image displays while editing but not in the post, so I'll try to...

So I am trying compute ##\displaystyle \int \sqrt{1+x^2}dx##. To start, I make the substitution ##u=\tan x##. After manipulation, this gives us ##\displaystyle \int |\sec u| \sec^2u ~du##. How do I get rid of the absolute value sign, so that I can go about integrating ##\sec^3 u##? Is there an...

Question: sqrt(x) cos(sqrt(x)) dx My try: Let dv = cos(√x) => v = 2√xsin(√x) and u = √x => du = dx/(2√x) Using integration by parts, we get ∫√x cos(√x) dx = 2√x√x sin(√x) - ∫(2√xsin(√x) dx)/(2√x) = 2x sin(√x) - ∫sin(√x) dx = 2x sin(√x) + 2 cos(√x) √x However, the answer given in the book...

It is a very simple question. If we have an expression like this one: x + y = 2 And we have to differenciate it, there is an algorithm that tells us how to do it. We have to find the relationship between the differentials of the given functions. To find them we have to substract the...

OK, I admit: this will be the most idiotic question I have ever asked (maybe: there could be more) So, I am aware of the differential calculus (derivatives) and the integral calculus (integrals). And separate from that, there is the first fundamental theorem (FFT) of the calculus which relates...

2000 $\tiny{206.q3.2}\\$ $\textsf{3. use the method of integrating factor}\\$ $\textsf{to find the general solution to the first order linear differential equation}\\$ \begin{align} \displaystyle \frac{dy}{dx}+5y=10x \end{align} $\textit{clueless !}$

Homework Statement I need to integrate ##\langle |v_x| \rangle = \int^{\infty}_0 |v_x| \sqrt{\frac{m}{2\pi kT}}e^{-mv_x^2/2kT}dv## For context this is a Maxwell Boltzmann distribution in one dimension, and I've actually been asked to calculate ##\langle v_x \rangle## which is given by...

When integrating terms including the imaginary unit i and operators like position and momentum, do you simply treat these as constants?

A simple method to find the potential of a conservative vector field defined on a domain ##D## is to calculate the integral $$U(x,y,z)=\int_{\gamma} F \cdot ds$$ On a curve ##\gamma## that is made of segments parallel to the coordinate axes, that start from a chosen point ##(x_0,y_0,z_0)##. I...

Homework Statement Evaluate the following line integrals in the complex plane by direct integration. Homework Equations Z= x+i y = Cos(θ) +i Sin(θ) = e^i*θ The Attempt at a Solution I'm not sure how to evaluated this by hand. I tried using Z= x+i y = Cos(θ) +i Sin(θ), and evaluating the...

Homework Statement $$f(x,y,z)=y$$ ; W is the region bounded by the plane ##x+y+z=2##, the cylinder ##x^2 +z^2=1##, and ##y=0##. Homework EquationsThe Attempt at a Solution Since there is a plane of ##y=0##, I decided that my inner integral will be ##y=0## and ##y=2-x-z##. But after this I have...

1. Homework Statement I'm trying to integrate this, the only variable is y the others(x,w) are all constants. Homework Equations The ways of integrating that I am familiar with are substitution, trigonometric substitution, by parts & partial fraction decomposition. The Attempt at a Solution...

I was looking for questions to practice normalizing a wave function, so I visited the following online pdf, http://people.physics.tamu.edu/syeager/teaching/222/hw1solution.pdf. The first question was to find the normalization constant, A of ψ(x) = A cos (2πx/L) for (−L/4) ≤ x ≤ (L/4). After...

I am trying to integrate the following triple integral, which has a heaviside function in the inner most integral:$$ \frac{16}{c_{4}^{4}} \int_{0}^{c_{4}} c_{3}dc_{3} \int_{c_{3}}^{c_{4}} \frac{dc_{2}}{c_{2}} \int_{0}^{c_{2}}f(x)\left ( 1-H\left ( x-\left ( c_{4}-a \right ) \right ) \right )dx...

Homework Statement Initially 5 grams of salt are dissolved in 20 liters of water. Brine with concentration of salt 2 grams of salt per lter is added at a rate of 3 liters per minute. The tank is mixed well and is drained at 3 liters a minute. How long does the process have to continue until...

I tried to put it in standard form as (dx/dy)+4x(1/(1+y))=y/(y+1). I get that the integrating factor is (y+1) but i am not sure if i am doing it right or what am I suppose to do next? I get (y+1) because the integrating of 1/(y+1) is ln(y+1) and since it has e, then ln cancels and i am left...

how do you integrate e^X-e^-x/e^-x+1 dx i am trying multiplying by e^x and trying to make it into no fraction but i am having no luck

Note: for easy reference, "serious" questions and such are italicized. I also should note that although the title says "science", I include many references to mathematics (I suppose one could argue that it is a science in some senses). Furthermore, in another thread that I've posted, some people...

Dear Sirs, I am currently calculating a velocity profile of an annular flow. Unfortunatelly I am not understanding the following step: [PLAIN]http://[url=https://postimg.org/image/vl256ffhj/] That seems the author had integrated the R constant. And remains the question: why had R been...

I have $$\int_{1}^{\infty} {x}^{-3} lnx \,dx$$ I choose to use integration by parts so I let $u = lnx$ and $dv = {x}^{-3} dx$. Therefore $du = \frac{1}{x} dx$ and $v = \frac{{x}^{-2}}{-2}$ Thus, what I need to evaluate is $$- \frac{-lnx}{{2x}^{2}} - \frac{1}{4 {x}^{2}} + C$$ As $x$...

Homework Statement Solve ##{dy/dx}-2xy=2x##Homework EquationsThe Attempt at a Solution Let ##P= -2x ## and Q= 2x, Integrating factor =## e^{-x^2} ## ##y.e^{-x^2} = ∫ 2x.e^{-x^2} dx## ##y.e^{-x^2}={x^2} e^{-x^2}+∫ 2{x^3} e^{-x^2}dx## since ##y.e^{-x^2} = ∫ 2x.e^{-x^2} dx## then...

\\text{w8.4.13 Integration by Parts} nmh{2000} $\displaystyle I=\int \sin\left({\sqrt{x}}\right) \ d{t} =2\sin\left({\sqrt{x}}\right) -2\sqrt{x}\cos\left({\sqrt{x}}\right)+C$ $\begin{align} \displaystyle u& = {\sin\left({\sqrt{x}}\right)} & dv&={1} \ dx \\ \\...

I need to define a function that integrates a function in some interval and returns its numerical value. I am not allowed to use built in functions for integrating in Mathematica. This is my code that won't work: http://pokit.org/get/?93856fe8f2070ba781028f8634b9ac3a.jpg This is a code from a...

If force isn't constant and you want to find the force of something at a specific time, you'd integrate right? For a specific question I came up with this F=ma Integral (m * da) da=dv/t Integral m * dv/t (m/t) * dv (m/t) * v So F = (m/t) * v Does this seem right? Or I'm I making illegal...

This is I think a really dumb question, but I never got it, why do we have that dot symbol when we integrate. Like in gauss's law, we have ∫E⋅dA . why is that ⋅ there? Thank you for your help

Hello! (Wave) I am looking at a proof where we have: $$\int_{-\infty}^{+\infty} |u|^{\frac{n}{n-1}} dx_1 \leq \left( \int_{-\infty}^{+\infty} |Du| dy_1 \right)^{\frac{1}{n-1}} \left( \prod_{i=2}^n \int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty} |Du| dx_1 dy_i\right)^{\frac{1}{n-1}}$$...

Homework Statement Using: \mathcal{L}\big\{t^n\big\}=\frac{n!}{s^{n+1}}\text{for all s>0} Give a formula for the Laplace transform of an arbitrary nth degree polynomial p(t)=a_0+a_1t^1+a_2t^2+...+a_nt^n Homework Equations \mathcal{L}=\lim_{b\rightarrow\infty}\int_{0}^{b}p(t)e^{-st}dt The...

Hi, eveyone have been struggling to do this problem for a long time now, figured it is something very simple I am missing so thought I should ask here. 1. Homework Statement Parker's solar wind equation is given after some manipulation as: (v - (Cs2 / v) dv/dr = 2 (Cs2 / r2) (r - rc ) where...

Hello, As you might discern from previous posts, I have been teaching myself: Calculus on manifolds Differential forms Lie Algebra, Group Push forward, pull back. I am an engineer approaching this late in life and with a deficient background in math. It is all coming together and I almost...

I've already completed the first question, but with number two, it's a different case. Here's my attempt: \frac { d{ v }_{ y } }{ dt } \quad =\quad -g\quad -\quad \beta { v }_{ y }\\ \frac { d{ v }_{ y } }{ -g\quad -\quad \beta { v }_{ y } } \quad =\quad dt\\ \int { \frac { d{ v }_{ y } }{...

Solve f'(x)*a(x)+a'(x)=1 For a(x) (there's another less important question at the bottom) Background behind equation (trying to find a function to integrate any e^f(x)): \int e^{f(x)}\,dx=e^{f(x)}*a(x) e^{f(x)}=e^{f(x)}*{f'(x)}*a(x)+e^{f(x)}*a'(x) 1=f'(x)*a(x)+a'(x)A few of my attempts...