What is parts: Definition and 838 Discussions

In science and engineering, the parts-per notation is a set of pseudo-units to describe small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractions are quantity-per-quantity measures, they are pure numbers with no associated units of measurement. Commonly used are parts-per-million (ppm, 10−6), parts-per-billion (ppb, 10−9), parts-per-trillion (ppt, 10−12) and parts-per-quadrillion (ppq, 10−15). This notation is not part of the International System of Units (SI) system and its meaning is ambiguous.

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  1. M

    The whole is greater than the sum of its parts. Or is it?

    Everything started from a very far-fetched line from a game, that got me into researching some interesting stuff. And eventually I arrived at this age-old question. I mean can this even be true? And I'm not talking about some trivial stuff, but rather on a more fundamental and universal level...
  2. J

    Minimum fencing when dividing triangle into 4 parts

    So I have an equilateral triangle an I want to divide it in 4 parts, all having the same area. This can be done in a multitude of ways of course. But assuming it's a garden and the division is about putting up a fence, which division uses the least fencing? Now I have two alternatives so...
  3. J

    Minimum boundary when dividing eqilateral triangle in 4 equal sized parts

    So I have an equilateral triangle an I want to divide it in 4 parts, all having the same area. This can be done in a multitude of ways of course. But assuming it's a garden and the division is about putting up a fence, which division uses the least fencing? Now I have two alternatives so...
  4. C

    Integration by Parts: Solving \int64x^2cos(4x)dx

    How would you go about doing this: \int64x^2cos(4x)dx The question specifically asks to integrate it by parts, so I integrated it that way a couple of times and came out with some long mess of sines and cosines, but it's not the right answer. Thanks.
  5. C

    Substitution and integration by parts

    Homework Statement Can anybody help me integrate x^3 e^{x^2} The Attempt at a Solution I can't see how to do it by substitution or integration by parts.
  6. V

    Integratiion by parts

    (2x+7)squareroot(7-x)dx from x=6 to x=7 i've been trying to solve this integral with the integration by parts formula but it won't work. would appreciate some help. would like to see the whole solution and not just the answer. (the answer should bee in fractions)
  7. R

    Real and Complex Parts of a Wave Function

    Homework Statement Just a snipit of one of my homework problems. I'm trying to find out what \Psi \frac{\partial \Psi^{*}}{\partial x} equals to help me find out what the probability current for a given free particle is. Homework Equations \Psi = Ae^{i(kx-\frac{\hbar k^{2}t}{2m})}...
  8. D

    Integrating By Parts: Is 4 Times Best for \int {x^4 e^x dx}?

    Hi. When evaluating an integral such as: \int {x^4 e^x dx} Is integrating by parts 4 times the best method, or is there a more efficient way? Thanks in advance, Dan.
  9. L

    Integration By Parts and Substitution

    [SOLVED] Integration By Parts and Substitution Short background; Took Calc 1 my senior year in high school. Got As all 4 quarters and found it quite easy. Freshman year comes around and I sign up for Calc 2. Turns out the only teacher teaching Calculus 2 for my fall and spring semester is a...
  10. rocomath

    Integration by Parts for Sec^5x

    \int\sec^{5}{x}dx i need a hint on this problem, my teacher told us that we prob. can't solve it with the method we've just learned. I'm not sure where to look in the book, I've looked through it but i don't know what is the best method. hint? pleasezz and i'll post all my work :D i...
  11. rocomath

    Integration by Parts (1) Help & Advice needed

    Picture. I don't know where I've gone wrong :-[ Any advice on how to tackle Integration by Parts? What should I subst. with what? Thanks! http://img528.imageshack.us/img528/9348/ibpkz5.jpg
  12. S

    Why are the poles of a magnet stronger?

    Are the force around the poles compressed, so it makes the poles of the magnet stronger than the other parts? Thanks.
  13. C

    Reduction formula/Integration by parts problem

    Homework Statement The problem asks me to: Determine a reduction formula for the stated integral (See Picture and problem at: http://garciarussellchem.angelfire.com/Photo/ Please help me out with this problem. I don't understand why they do not include an extra r in the denominator...
  14. T

    How to solve the integral using integration by parts?

    Homework Statement Hi, I'm trying to solve http://img204.imageshack.us/img204/7199/untitledke0.png in terms of I(n-2) but I'm not exactly sure where to start/what to do :uhh:
  15. F

    How to integrate e^x cos(x) using parts?

    Is it possible to intergrate e^x (cosx) i wondered because i tried to intergrate it by parts, but ended up going round in circles. I wondered because i had this question and I am stuck on how to do it :) http://img505.imageshack.us/img505/320/frfbc8.png
  16. S

    How to find the DImensions of all the parts of the device

    Homework Statement As picture attached .We need to find the dimensions of all the parts that are Pin(A),Jaw(B and C), NUt (D) , Handle (E) .The jaw B is fixed and C is free to move towards B.There is a force T=1779.261 N on Jaw C.Secondly there is a human force involved in turning the handle...
  17. S

    Help with an integration by parts problem

    integration problem :( Homework Statement int from 1 to 1/4 of [cos(pi*sqrt(t))] / sqrt(t) dt Homework Equations The Attempt at a Solution I tried using integration by parts used u = cos pi (sqrt(t)) and dv = sqrt(t), but got a really messy number as int of vdu so I tried u =...
  18. R

    Integrate (ln(x))^2 - Steps and Solution

    intergrate (ln(x))^2 so i set u=(lnx)^2...which makes du=2lnx(1/x) then i set dv=dx...which makes v=x according to the formula for integration by parts i have x(lnx)^2- integral x(2lnx)(1/x) simplifying it i get x(ln)^2-2intergral lnx and here is where i am stuck...what i the...
  19. F

    Parts of a Photon: Exploring Time Dilation & Acceleration

    I've been looking at the parts of a photon as it moves at the speed of light and how this affects the photon it's self. I have encountered a few things such as the need for the photon to start spinning as it moves through gravitational fields ECT. But I have recently found 2 things that are very...
  20. I

    Integration by Parts: Evaluating e^xcos3x dx & x^2/(2(1+x^2))

    Homework Statement Hi, I'm trying to evaluate the integration of (e^x)cos3x dx, by using integration by parts. I've already done a couple of similar questions on integration by parts but this one seems to puzzle me. Homework Equations The answer is supposed to be (e^x/10)*(cos3x +...
  21. B

    Integration by Parts - Proving Equations for m and n > 1

    Hi, J(m,n) = \int_0^{\frac{\pi}{2}} \cos^m \theta \sin^n \theta d\theta First of all I had to evaluate the following ( I don't know what the correct answers are but here are my calculations: J(0,0) = [\theta]_0^{\frac{{\pi}{2}}}=\frac{\pi}{2} J(0,1) = [-\cos...
  22. P

    What Went Wrong with My Integration by Parts?

    Hello there. I feel like this isn't the right answer, but I'd like some verification as to where exactly I went wrong! 1. Homework Statement is \int_{0}^{pi}x^2cos x dx 3. The Attempt at a Solution went something like this: u=x^2 dv=cos x dx du=2x dx v=\int_{0}^{pi}cos x dx= sin x...
  23. A

    Efficient Integration by Parts: Solving \int x^2*cosx dx with Step-by-Step Guide

    Homework Statement \int x^2*cosx dx Homework Equations The Attempt at a Solution Okay, so I started by making... u=x^2 du=2x dv=cos(x) v=-sin(x) Then I made the rudimentary equation: \int x^2 * cos(x) dx = -x^2*sin(x) + \int 2x * sin(x) dx Then I took the last integration problem (the one...
  24. C

    Integration by parts ln(x^2+14x+24)

    Homework Statement ∫ ln(x^2+14x+24) Homework Equations Integration by parts: ∫ udv = uv - ∫ vdu The Attempt at a Solution I chose u = ln(x^2+14x+24) and dv = dx therefore du = 2x+14/x^2+14x+24 and v = x Then once I substitute, I get: ∫...
  25. L

    How can I evaluate this integral using integration by parts?

    Homework Statement indefinite integral dx/((e^x)(sqrt(1-e(-2x)))) using integration by parts evaluate the integral. Homework Equations integral u*dv = u*v- integral v*du The Attempt at a Solution To be completely and entirely honest i am not even sure where to start with this...
  26. H

    How to integrate (1/x*sqrt(4x^2 -1)dx using parts or trig?

    Homework Statement (1 / x * sqrt(4x^2 - 1))dxHomework Equations done by parts/trig?The Attempt at a Solution 1 = c 2x = b sqrt(4x^2 - 1) = a sin(theta) = 2x sin(theta) / 2 = x -(1/2)*cos(theta) d(theta) = dx cos(theta) = -2*sqrt(4x^2 - 1) I am not sure what to do about the x? Can I just...
  27. F

    Parts for Project: Finding What You Need for Success

    First, hello all! Sorry if this is in the wrong forum (or wrong site, even), but I'm not sure where else to go, and I stumbled upon here doing some research (for project ideas). Feel free to delete this if it's off-topic. I am building a simple research project, and need some help choosing...
  28. O

    INtegration by substitution followed by parts:

    ... of (x tan^2 x). i don't know how to do it. pls help
  29. M

    Integration by parts with my work

    Homework Statement integrate arctan(1/x) Homework Equations The Attempt at a Solution z=arctan(1/x) dx=-dz(x^2-1) now its the integral of z(x^2-1)dz let u =X^2-1 du=2x dv=-udu v=-u^2/2 integral=(x^2-1)(-u^2/2) - int (-u^2)(2x) this is where i got stuck but i...
  30. M

    Integrating arctan(1/x) with Integration by Parts

    im having a bit of trouble, can anyone help me integrate arctan(1/x) using integration by parts? thanks
  31. C

    Integration by Parts: Evaluate ∫ 1 ÷ (16 + x2) dx

    Homework Statement Use integration by parts to evaluate the integral: ∫ 1 ÷ (16 + x2) dx Homework Equations ∫ u dv = uv - ∫ v u' du The Attempt at a Solution That's the problem, I don't know how to start. How would I divide up 1/(16 + x2) into two? So there would be a value for u...
  32. N

    Integration by Parts with a Touch of Trig

    Hey y'all. I'm new to the forum, and have a problem that I've been working on all night long. I'm having issues previewing the Latex, so bear with me. I'll post the work I've done so far if the problem code shows up. Thanks. \int{\sin^{\frac{3}{2}}2\theta\cos^{3}2\theta} d\theta Now, the...
  33. A

    Solving Integration by Parts Problem from 1 to 4

    Homework Statement Hi, I've been having trouble solving the following problem, please help me. Question: (integration from 1 to 4) e^(x^(1/2))dx Homework Equations The Attempt at a Solution So far, i have done the following: u = e^(x^(1/2)) du =...
  34. C

    Heat equation and Theta, Parts I-III

    I am taking the liberty of collecting mathwonk's "short course" for some followup comments/questions, since this topic is IMHO more interesting than the context in which it first appeared. (Hope this is OK under PF rules!). Part I: Part II: Part III: How annoying, Part IV won't...
  35. T

    Integration by parts and simplifying

    Hi, I have been working on this problem for the longest time and have just run in circles with it. I am thinking the answer is obvious but for some reason I am missing it. I need to find \int \frac{ln(x)}{x^2} dx I know that I need to use integration by parts and have tried a number of...
  36. L

    Integration by parts r e^r/2 dr

    i know this is integration by parts so here is the problem I am currently confused on how the get an answer r e^r/2 dr I know I the formula is int udv= uv - int du v what i am not getting is what to use for this one. I figured e^r/2 = v and du = r so u= r^2/2 and what...
  37. L

    Can You Calculate Factorials for Non-Integer Numbers Using Integration by Parts?

    integral of (e^(2x))(cos3x)dx I get 1/2e^(2x)sin2x - 3/2integral(e^(2x)cos3xdx) what do i do next?
  38. B

    Integration by substitution and by parts

    I did a few problems in integration by parts. There are two that I just can't seem to get. I've tried every type of subsitution or part I can think of. 1. e^sqrt(x) 2. sin (ln x)
  39. R

    Integration by parts problem

    "Evaluate the integral [0,1] x^3/sqrt[x^2 + 1] by integration by parts" I know I have to use the integration by parts equation, but I don't know what to make u and what to make dv..
  40. M

    Arranging friends, permutations, have the answer, not sure on some parts

    Hello everyone. The book has this problem: (h) You are arranging six of your friends Alice, Bob, Charles, Diana, Francine, and George, in a row so that you can take their picture. (i). Alice and Bob have had a fight and refuse to stand next to each other. How many ways are there to...
  41. S

    Integration by Parts: Solve y(1+y^2)^1/2 dy

    integral y(1+y^2)^1/2 dy can someone help me with this? Thanks.
  42. mbrmbrg

    Integrating, probably by parts

    I have the expression \int{x(\ln{x})^3dx} I thought I had a quick way to integrate by parts but it turned out that I had accidentally evaluated \int{x\ln{x}dx} instead. Revisiting \int{x(\ln{x})^3dx}, I wanted to start by making a strange substitution, wherein u=ln(x), du=1/x dx, and x=e^u...
  43. mbrmbrg

    Solving Integration by Parts Problem: \int\frac{dx}{a^2-x^2}

    Problem: \int\frac{dx}{a^2-x^2} My Work: \frac{1}{a^2-x^2} =\frac{1}{(a+x)(a-x)}=\frac{A}{a+x}+\frac{B}{a-x}} 1=A(a-x)+B(a+x) If x=a, then 1=2Ba so B=\frac{1}{2a} Thus 1=A(a-x)+\frac{1}{2a}(a+x) if x=0, then 1=Aa+\frac{1}{2} so A=\frac{1}{2a} SO \int\frac{dx}{a^2-x^2}...
  44. T

    Integral: e^{(ax)} cos(bx) - Solve with Integration by Parts

    Hi all, I am having problems with the integral: \int e^{(ax)} cos(bx) dx I have got to \frac{e^{ax} sin(bx)}{b} - \int \frac{a e^{ax} sin(bx)}{b} dx After this I can only see myself going around in circles. Any help would be appreciated. :smile: Cheers, The Bob (2004 ©)
  45. J

    Integration do i use substitution or parts?

    Hi, i am stumped on how to start this: integration of sin(ROOT(1 + x)) so, basically sin of square root 1 + x thanks James
  46. L

    Integration by Parts: Troubleshooting the Formula for x cos 5x dx

    kay I am having difficulties with this.. Knowing the gerneral formuala of |uv'=uv- |vu' i using a nonehomework question i was trying to make sure i had it down pat was having problems.. | x cos 5x dx but for some reason i don't get the right answer when it done... If I have u=x...
  47. S

    Intergration by parts question from A2 core 4

    I need to find the integral of (x^2) 2 (secx)^2 tanx dx said aloud: x squared times by two times by sec squared x times by tan x I tried to use the [tex] function but failed misserably, hope you understand what i mean from what I've written above.
  48. C

    Efficiently Evaluating \frac{1}{x\ln x} Using Integration by Parts

    How do you evaluate \frac{1}{x\ln x} by integration by parts. I tried doing this doing the following: u = \frac{1}{\ln x}, du = \frac{-1}{x(\ln x)^{2}}, dv = \frac{1}{x}, v = \ln x . So I get: \int udv = uv-\int vdu = 1 + \int \frac{1}{x\ln x} = \int \frac{1}{x\ln x} . I know the answer...
  49. F

    Solving Integral Using Integration by Parts

    I'm doing a problem where I'm supposed to use integration by parts. I have: Integral ln(x+3)dx u=ln(x+3) dv=dx du=1/(x+3) v=x integral ln(x+3) = xln(x+3) - integral x/(x+3) That's as far as I've gotten. I know that I should be able to find the integral of x/(x+3)...
  50. K

    Classical problem: projectile exploding into two parts with one part going down

    So my problem is: a mass M that is fired at 45 degrees with KE E_0, at the top of the trajectory, projectile explodes with additional energy E_0 into two parts, the first fragment travels straight down , what is the velocity of the the first and the velocity and direction of the second part...
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