# What is Integrate: Definition and 650 Discussions

IntegRate was a software product written in C++ based on a pipe-lined high performance architecture for handling batch rating of telecommunications using call detail records (CDR), developed by the German software company Solution 42.

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1. ### How can I calculate the cumulative mass of a disk using disk mass density?

I want to find the cumulative mass m(r) of a mass disk. I have the mass density in terms of r, it is an exponential function: ρ(r)=ρ0*e^(-r/h) A double integral in polar coordinates should do, but im not sure about the solution I get.
2. ### A How to integrate this equation?

Hello, can someone help me to solve the following differential equation analitically: $$\frac{2 y''}{y'} - \frac{y'}{y} = \frac{x'}{x}$$ where ##y = y(t)## and ##x = x(t)## br Santiago
3. ### A Need help with an integral -- How to integrate velocity squared?

The integral is this one: ##\int (\dot x)^2 \, dt,## With ##x=x(t). ## I don't know how to solve that integral and I haven't find nothing to read about on how to proceed with this kind of (implicit function?) integrals without having the initial function.
4. ### Integrate or divide the input impedance for transmission lines in series?

Here I list my problem in the attachment.
5. ### Using ODE45 on Matlab to Integrate A Problem

I got the answer for this question but I was wondering about stepsize when it comes to a problem like this? Is there a way to change the step size? Would my step size change in line 20, or would it change in line 3? I tried changing line 3 to be t=0:100:17.1 but then I get a error message, so...
6. ### Integrate ##\int\sqrt{4+x^2} dx##

still typing...checking latex
7. ### I Why can't we just integrate a simple function?

Can anyone explain to me why the second one is the right? (See the attachment)
8. ### Why Does My Integration Over a Sphere Give Incorrect Results?

##\iiint 3 dr d\rho d\phi## The volume of a sphere is ##4\pi /3 r^3## so naturally the answer is ##4 \pi R^3## But when I integrate I do: ##3 \iint r |_0^R d\rho d\phi## ##3R \int \rho |_0^{2\pi} d\phi## ##6R\pi * \phi |_0^\pi = 6R\pi^2## What am I doing wrong?
9. ### I How Do You Integrate Expressions Like These?

How do you you integrate expressions like these? 1. ##\frac{1}{\sqrt{x^3 + 3}}## 2. ##\frac{1}{\sqrt{x^4 + 3}}## 3. ##\frac{1}{x \sqrt{x^5 + 3}}## 4. ##\frac{1}{x^2 \sqrt{x^3 + 3}}## 5. ##\frac{1}{x^3 \sqrt{x^3 + 3}}## 6. ##\frac{1}{x^4 \sqrt{x^3 + 3}}## 7. ##\frac{1}{x^5 \sqrt{x^3 + 3}}##...
10. ### How to Integrate [1/(x^2 + 3)] dx?

What is ##\int \frac{1}{x^2 + 3} \ dx##? This is my attempt: ##x = \sqrt{3} \tan \theta## --> ##dx = \sqrt{3} \sec^2 \theta \ d\theta## ##x^2 + 3 = (\sqrt{3} \tan \theta)^2 + 3## ##= 3 \tan^2 \theta + 3## ##= 3 (\tan^2 \theta + 1)## ##= 3 \sec^2\theta## ##\int \frac{1}{x^2 + 3} \ dx = \int...
11. ### MHB Integrate 3/(x(2-sqrt(x))) - No Partial Fractions

integral of 3/(x(2-sqrt(x))) using u=sqrt(x)? But not using partial fractions
12. M

### Use Python to integrate a function constructed in Mathematica

Hi PF! I followed someone's help on here and have the following code in python that performs monte carlo integration from math import * from random import * def integrate(alpha): # MONTE CARLO INTEGRATION OVER NON-RECTANGULAR DOMAINS def f(pt): # RETURN INTEGRAND AS FUNCTION...
13. ### Integrate along curve, book has wrong answer?

So it's basically a half circle with radius a. y = asin(t) $$\int_0^{\pi} asin(t) dt = -acos(t) |_0^{\pi} = 2a$$ The book says the answer is ##2a^2##, but maybe that's wrong?
14. ### Integrate acceleration when a = f(v)

Mentor note: Moved from a technical forum section, so missing the HW template. Summary:: Integrate acceleration when a = f(v) when separation of variables is not trivial, ie a = k +v^2 When acceleration is a function of velocity, ie there is a friction force, you would separate the variables...
15. ### B Helping a 5-Year-Old Integrate a Function in Kindergarten

A newbie who knows basic math is helping a five year old do his kindergarten project. The boy has to integrate a function ##f(x,y)## over the boundary of the first quadrant denoted ##\partial \Omega## where ##\partial\Omega = \{ x=0, y\geq 0 \} ∪ \{ x\geq 0, y=0 \} ## How would I explain to...
16. ### I How Do You Integrate 1/√(x^3 + x^2 + x + 1) dx?

How do you integrate ##\frac{1}{\sqrt{x^3 + x^2 + x + 1}} \, dx##? Please give me some hints and clues. Thank you
17. ### How To Integrate 1/[sqrt (x^2 + 3x + 2)] dx?

How do you integrate ##\frac{1}{\sqrt{x^2 + 3x + 2}} dx##? I had tried using ##u = x^2 + 3x + 2## and trigonometry substitution but failed. Please give me some clues and hints. Thank you mentor note: moved from a non-homework to here hence no template.

33. ### I How do we integrate x^2/(e^x - 1) from xg to infinity?

How do we integrate this function? It is possible if the range is from 0 to infinity, but from xg to infinity? This equation comes from page 512 of the 1961 paper by William Shockley and Hans J. Queisser.
34. ### A How to integrate this function?

Hello I am studying Landau Mechanics (3rd ed.) In chapter III Integration of the Equations of Motions §15. Kepler's problem page 36 M(angular momentum), m(mass), E(mechanical energy), and α are constant. How to integrate it? Please help me...
35. M

### Mathematica What technique to integrate this function?

Hi PF! Attached are two plots of the same function, one uses a parameter ##a=89.9## and the other uses ##a=89+9/10##. As you can see both functions are very different. Also, using NIntegrate over each gives two different outputs respectively, ##-6.91846*10^{12},-6.91949*10^{19}##. My question...
36. ### How to integrate this function?

Homework Statement I've got to integrate the following $$\int dx =\int \frac {d\phi} {\phi \sqrt {1 - \phi²}}.$$ Homework Equations [/B] I already know the answer but not how to get it. The answer that I got from solution is ## x = \operatorname {arcsech}{\phi} ##. The Attempt at a...
37. ### I EoM via varying action - covariant derivative when integrate

##\int d^4 x \sqrt {g} ... ## if I am given an action like this , were the ##\sqrt{\pm g} ## , sign depending on the signature , is to keep the integral factor invariant, when finding an eom via variation of calculus, often one needs to integrate by parts. When you integrate by parts, with...
38. ### I How do you integrate eqns with indices?

Hello, I just want to clarify some things with a simple exercise: I have the equation ## \frac{\partial^2 f}{\partial A^\mu \,\partial A^\nu} = 0## and I want to integrate it once assuming that ## f=f(A^1,A^2,...,A^n)=f(A^\rho) ##. I think the solution should be ## \frac{\partial f}{\partial...
39. ### How did 27.84x10^-6 become 3.593x10^4? Integration Help

1. The problem statement, all given data I've been working through one of the lessons for my HNC and I'm totally stuck on how they got from 27.84x10^-6 to 3.593x10^4. I can follow it all fine including the integration after that section it's just the inbetween that I can't seem to get my head...
40. ### I Integrating a Function over a Torus Contour

I'd like to integrate a function over a closed circle-like contour around an arbitrary point on a torus and I assume I would use the expression: $$\int_{t_1}^{t_2} f(x,y,z) \sqrt{x'(t)^2+y'(t)^2+z'(t)^2}dt$$ And I cannot come up with an explicit parameterization of the variables in terms of...
41. ### A Integrate f(x) = tanh(c*x^b)? Wolfram says not possible ....

I'm working on a guitar amp distortion emulation which is waveshaping based on the following equation: f(x)= x/|x| * tanh (c * |x|^b) This looks like this: So the idea is values of "x" (the raw guitar signal amplitudes) are fed in and get soft then hard limited to an output of y=+/-1. As...
42. M

### MATLAB Is there a faster way to symbolically integrate Legendre polynomials?

Hi PF! I'm doing several operations involving integrating Legendre polynomials. Since I am trying to loop through, my approach is something like N = 5; a = 0.5; x =linspace(-1,1,100); for k=1:N v(:,k) = legendreP(k+1,x)-legendreP(k+1,a)/legendreP(1,a)*legendreP(1,x); end% for j where I...
43. ### How to know which way to integrate?

Homework Statement Please see the attachment. This isn't a question, but more so my understanding of the book. Please read the middle paragraph. So I'm suppose to take an integral of cos(x)sin(x) Wolfram and my book give the answer as -(1/2)cos(x)^2, but when I did it I got it as...
44. C

### I Integrate translated gaussian function by change of variable

I want to integrate this: \int_0^∞ re^{-\frac{1}{2σ^2} (r-iσ^2q)^2} \, dr. If I change the variable r into t with this relation:r-iσ^2q=t, then the integral becomes\int_{-iσ^2q}^∞ (t+iσ^2q)e^{-\frac{1}{2σ^2} t^2} \, dt so it seems I cannot use the famous gaussian integral formula. But I got the...
45. ### I What Is the Integration Process for tan(2x) dx?

This is the continuation of the below thread: https://www.physicsforums.com/threads/what-is-integral-tan-2x-dx.856530/ Can someone please tell me how to integrate tan 2x dx?
46. M

### How to Integrate 1/sqrt(1+x^2) dx | Step-by-Step Solution

Homework Statement Integral of 1/sqrt(1+x^2) dx Homework Equations sin^2theta`+cos^2theta=1 1+tan^2theta=sec^2theta The Attempt at a Solution I plugged x=tant --> dx=sec^2t dt => integral of 1/sqrt9(1+tan^2t) sec^2t dt = integral of t = tan^-1t + C However, another answer I've seen involves...
47. ### Integrating 1/(x+x^3+2): Simplified Steps & Techniques

Homework Statement integrate 1/(x+x^3+2) Homework EquationsThe Attempt at a Solution I have tried to use partial fraction but the process is very complicated. Are there any faster methods? It is one of the ten questions in a 50 minutes elementary level test. Here is my attempt, ∫ 1/(x^3+x+2)...
48. ### B Rule to integrate a function with respect to its derivative

Hello all, I was just wondering if there is any rules for integrating a function with respect to it's own derivative. That is to say ##\int _{ }^{ }f\left(x\right)d\left(f'\left(x\right)\right)## or ##\int _{ }^{ }yd\left(\frac{dy}{dx}\right)## Thank you in advance for your time :)
49. ### When to Integrate Charge Enclosed for Gaussian Surfaces?

Hello, I was looking over my notes and I was trying to figure out when we integrate Q enclosed when Q = ρ*d(volume). If there's one thing I've learned from physics II you only integrate when a field is non-uniform. I'm just wondering how we know when it's uniform (usually the problem will tell...
50. ### How can you use the tabular method to integrate xcos(x^2)

Homework Statement This is not a homework but since asked me I'm posting it here. I know how to intergrate by parts and can do this using formula But I'd like to do this using the tabular method Question Integrate xcos(x^2) using tabular methodHomework Equations The table with derivative on...