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. A

    Problem with Integrating by parts

    I would like to integrate by parts this term- \mu^2 (\nabla^2)^{-1} (\nabla\times B)\dot{B} Here B is a vector and \dot{B} is the time derivative of B. And \mu is just a constant. Can anyone help me?
  2. B

    Integration by parts with a dxdy

    Homework Statement The functional ##I(u,v)=\int_\Omega F(x,y,u,v,u_x,u_y, v_x,v_y)dxdy## The partial variation of a functional is given as ## \displaystyle \delta I =\int_\Omega (\frac{\partial F}{\partial u} \delta u+\frac{\partial F}{\partial u_x} \delta u_x+\frac{\partial...
  3. B

    Integration by Parts in Calculus: Understanding the Process and Its Applications

    FOlks, I am self studying a book and I have a question on 1)what the author means by the following comment "Integrating the second term in the last step to transfer differentiation from v to u" 2) Why does he perform integration by parts? I understand how but why? I can see that the...
  4. R

    Which parts of Calcs I-III are most important to remember for higher level math?

    Hi, I realize that this might be a silly question to ask without some proper background so: I'm a rising sophomore who is reviewing Calculus I-III right now. I first took Calculus as a junior in high school under the AP Calculus BC curriculum. I then took multivariate calculus and a semester of...
  5. S

    Simple Integration by Parts Question

    Homework Statement integral of e^-xsinxdx Homework Equations uv-/vdu The Attempt at a Solution u=e^-x du = -e^-xdx v=sinx dv=cosxdx e^-xsinx-/(-e^-x)sinx =e^-x(sinx+cosx) Wolfram alpha is telling me that the indefinite integral is actually "-1/2e^-x(sinx+cosx)" where did...
  6. L

    Hard definite integration by parts question,

    Homework Statement Integral, from 0 to 1, y/(e^2y) Homework Equations Use integration by partsThe Attempt at a Solution I need integration by parts. The answer is 1/4-3/5e^-2. But I got 1/2 and it all makes sense to me, so tell me what I got wrong. I put u=e^2y du=2e^2y dv= 1/e^2y dy (did...
  7. L

    Hard integration by parts question,

    Homework Statement Integral, from 4 to 6, 1/(t^2-9) dt Homework Equations please use my approach to solve it, like with cosh and whatnot The Attempt at a Solution Integral, from 4 to 6, 1/(t^2-9) dt so I multiplied the top and bottom by square root of 9. which got me...
  8. Psinter

    Can't integrate by parts an integral with a fraction inside

    Homework Statement In the section of the book of integration by parts, there is an exercise that I don't even know how to tackle anymore. It's this: \int \frac{xe^{2x}}{(1+2x)^2} dx Homework Equations {uv} - {\int v{du}} The Attempt at a Solution u = x ; du = 1...
  9. Z

    Understanding Symbolic Math in MATLAB: Real and Imaginary Parts

    I have such MATLAB problem: I create variables R1 RF R2 and w so: syms RF R1 R2 w then I write expression: 3*R1*w*(RF + 200)/((R2*w*29*i + 3)*(3*R1*w - 2*i)) which gives: (3*R1*w*(RF + 200))/((3*R1*w - 2*sqrt(-1))*(R2*w*29*sqrt(-1) + 3)) why sqrt(-1) and not i? furthermore? if I want real part...
  10. B

    Integration by parts if f' ang g' are not continuous

    The Integration by Parts Theorem states that if f' and g' are continuous, then ∫f'(x)g(x)dx = f(x)g(x) - ∫f(x)g'(x)dx. My question is, are those assumptions necessary? For example, this holds even if only one of the functions has a continuous derivative (say f' is not continuous but g'...
  11. R

    U substitution and integration by parts

    I would think because of this The following problem: At this stage they should use integration by parts: However, maybe integration by parts is only useful when one of the parts is e^x ln or a trigonometric formula.
  12. Ranger Mike

    Manufacturing Defects - not all parts are equal

    One of the things all the pros do is to check all parts before assembly..good tip for all racers..my life long round track driver, “ Krash” had a real head scratching problem. The starter he ran for years was now not turning over the engine. It was hanging up at the same point of rotation. We...
  13. R

    Integration by Parts and Substitution: Solving Complex Integrals

    Homework Statement Homework Equations uv - integral of vdu The Attempt at a Solution They don't seem to be using the integration by parts formula here. I don't understand why why they don't have a value for what z equals. dz = eu. well, what does z equal. I would think it...
  14. R

    Helium tank filling parts to a specific pressure?

    Homework Statement I have a tank that has 8000 cubic feet of helium in it. I have parts I'm filling to a gage pressure of 0.5 bar. The parts have a volume of 0.05ft^3. How many cubic feet of helium are in each part? Temperature is constant. Homework Equations I'm not sure if I'm missing...
  15. B

    Turbine-powered subway train (3 parts)

    Hi, For my Writing for Engineers class I have decided to take on a feasibility inquiry: "Is it possible to power a NYC subway train using wind turbines atop that same train?" (provided that a NYC subway train requires 2.1 MW of power to run at 55 mph) Now, I have come to the conclusion that...
  16. O

    Integrating ln(x+1)/(x^2+1) using recursive integration by parts

    Hi, I need to find ∫ln(x+1)/(x^2+1)dx I think it might involve recursive integration by parts, so first I set: u=ln(x+1) dv = 1/(x^2+1)dx du=1/(x+1)dx v=ArcTan(x) ∫ln(x+1)/(x^2+1)dx = ArcTan(x)Ln(x+1) - ∫ArcTan(x)/(x+1)dx Then I integrated by parts again, so...
  17. E

    Parts List = Bill of materials?

    Is a part list equivalent to a bill of materials?
  18. DryRun

    Solving Complex Equation: Real & Imaginary Parts of z=x+iy

    Homework Statement Given that the real and imaginary parts of the complex number z=x+iy satisfy the equation (2-i)x-(1+3i)y=7. Find x and y. The attempt at a solution I know it's quite simple. Just equate the real and imaginary parts, but i checked and redid it again, but the answer still...
  19. Y

    Coefficient of kinetic friction on 2 different parts

    Homework Statement When the mass M is at the position shown, it has a speed v0 = 2.17 m/s and is sliding down the inclined part of a slide. The mass reaches the bottom of the incline and then travels a distance S2 = 2.45 m along the horizontal part of the slide before stopping. The distance S1...
  20. J

    Drawing and Computing Moment Diagrams by Parts: Tips and Rules

    Urgent Help Please! Just want to ask some rules/ tips in drawing MOMENT DIAGRAM BY PARTS and COMPUTING FOR THE MOMENT OF THE AREA OF THE MOMENT about a particular axis. Here's the step I typically do: 1. Get the reactions. 2. Plot the moment diagram of EVERY force. (that's why it's...
  21. B

    Parts to include in a wavefunction

    Hi all, I was wondering if anyone could help me with some general rules for which parts one should include in a wave function when trying to determine symmetry. In simple cases, we see things like $$\psi_{\rm space}\psi_{\rm spin},$$ and in more complicated cases we see $$\psi_{\rm...
  22. I

    Using integration by parts to prove reduction fomula

    Use integration by parts to prove the reduction formula: int(sec^n)x dx = (tan(x)*sec^(n-2)*x)/(n-1) + [(n-2)/(n-1)]int(sec^(n-2)*x dx n /= 1 (n does not equal 1) I used "int" in place of the integral sign. This was a problem on the corresponding test from the cal A class I am from...
  23. S

    Integration by parts involving an unknown function

    Homework Statement I have attached a picture including 2 equations: (2.13) and (2.14) I don't understand how they got from (2.13) to (2.14) using integration by parts Homework Equations The Attempt at a Solution For the integral: \int_{\tau_0}^t\sigma(\tau)d\tau=...
  24. P

    Splitting Infinite Series into Real and Imaginary Parts

    I need a quick reminder that this is (hopefully) true: Let \sum a_n be an infinite series of complex terms which converges but not absolutely. Then can we still break it up into its real and imaginary parts? \sum a_n = \sum x_n + i\sum y_n
  25. A

    MHB Divide a line segment into three equal parts

    is there a way to divide a line segment into three equal parts using just compass and ruler ? I heard that there is not a way and there is a proof for that is that right ?
  26. H

    Splitting a function into odd and even parts

    Hi, I've been looking at Fourier transforms, odd and even functions and such recently. But I'm a little confused about how exactly you split a function up. I know the general forumla and seen the derivation, however when i do it with a proper function i never seem to get the correct answer. Was...
  27. C

    Units assistance for loading of parts

    Hi all, I am building a model in Abaqus and wondered if somone could assist with the units I need to enter. I have built my parts using mm as the dimension, i.e. part is 10 units (mm) wide. (To clarify this can also be entered as metres as in 10e-3, however I chose to be consistent with...
  28. idir93

    Integration by parts can you solve this problem please

    calculate : ∫x²e-x3dx by parts please i need details :) thank you very much
  29. I

    An integral by parts problem - please advise

    Homework Statement The function is increasing and has a inverse f^-1 Also assume f′is continuous and f'(x) > 0 over the state interval of integration [a,b] PLEASE NOTE! a is lower limit, b is upper limit (same for alpha and beta symbol later on) Used integration by parts to show that: \int...
  30. Roodles01

    Integrate 1/x(2/3) - Solve for 3 Cube Root 3

    knowing the standard form for integration by parts is ∫ f(x)g'(x) dx = f(x)g(x) - ∫f'(x)g(x) dx I have what is an innocuous looking part of an equation which I can't solve. the f(x) part in this case is; ln(5x) which is easy enough i.e. 1/x the second part 1/(x(2/3)) is the bit I...
  31. M

    On the integration by parts infinitely many times

    greetings . it's known that if g(x), f(x) are two functions ,and f(x) is sufficiently differentiable , then by repeated integration by parts one gets : \int f(x)g(x)dx=f(x)\int g(x)dx -f^{'}(x)\int\int g(x)dx^{2}+f^{''}(x)\int \int \int g(x)dx^{3} - ...
  32. N

    Complex Analysis - Values of Real and Imaginary parts

    Homework Statement Simplify in terms of real and imaginary parts of x and y and sketch them. 1) Re \frac{z}{z-1} = 0 2) I am \frac{1}{z} ≥ 1 The Attempt at a Solution 1) \frac{x + iy}{x + iy -1} = 0 Am I allowed to just vanish the imaginary components here and have \frac{x}{x...
  33. M

    I with the Doppler Effect - I solved 2/3 parts of the problem

    I solved for parts and a and b of this problem and need someone to check the answers for me and help me with part c. A) 467.5 Hz B) 5.45 m/s Jane is standing on the platform waiting for the train. The train approaching the platform from the north at 20 m/s blows its whistle when it is 100 m...
  34. L

    Integrating by parts Maxwell Lagrangian

    I attached a file that shows the free EM action integral and how it can be rewritten. I would like to know how to go from the first line to the second. I have to integrate by parts somehow, and I know surface terms get thrown out, but I do not know how the indices of the gauge fields should be...
  35. H

    Automotive How performance car parts influence torque vs horsepower?

    I am currently majoring in mechanical engineering at Texas A&M after having completed my associates degree in automotive technology (4.0gpa) while i'v been fixing cars at Firestone Autocare. Its odd that i rarely find anyone who knows a thing about the physics of energy efficiency and the...
  36. S

    Integration - u substitution problem (Integration by parts?)

    Homework Statement Find the integral of 3x* (2x-5)^6*dx, let u= 2x -5. Homework Equations Im not sure if i am meant to use integration by parts or not?? I was able to do previous questions of the topic just using u sub to get rid of the first x variable. The Attempt at a Solution...
  37. K

    Integration by parts, where am I going wrong?

    Homework Statement \int_{1}^{2} x^2 e^{x} dx Homework Equations Integrating by parts. Writing out chain rule, integrating both sides and rearranging gives ∫f(x)g'(x) dx = f(x)g(x) - ∫f'(x)g(x) dx The Attempt at a Solution \int_{1}^{2} x^2 e^{x} dx = \left[x^2...
  38. T

    Evaluate the integral using integration by parts?

    Homework Statement Evaluate the integral. Integral = x f(x) dx from 0 to 1 when f(1) = 6, f'(1) = 7. Answer choices: A. 11/6 + 1/6 integral from 0 to 1 x^3f''(x)dx B. 11/12 - 1/6 integral from 0 to 1 x^3f''(x)dx C. 11/3 + 1/2 integral from 0 to 1 x^2f'(x)dx D. 11/3 - 1/2 integral from 0 to 1...
  39. D

    When exactly does the tabular method for integration by parts fail?

    I found this interesting but different way to solve integration by parts problems on the internet: http://imageshack.us/photo/my-images/854/integration20by20parts2.jpg/ It seems to work well for me when doing most textbook problems, except when the integrand contains a natural logarithm. I just...
  40. D

    Complex Numbers - Forms and Parts

    Hi, I have a complex number and understand that the rectangular form of the number is represented by s = σ + jω, where σ is the real part and jω is imaginary. I am having trouble locating them in the number below: I know that "2" is a real number, and the numerator is imaginary...
  41. S

    Integration by parts - Does this make sense?

    I'm confused. I was making up some of my own problems involving higher powers of x to integrate. For example: \displaystyle\int x^5 e^{5x}dx I set about going about finding \frac{dy}{dx} up to \frac{d^6y}{dx^6}. u=x^5 \frac{du}{dx}=5x^4 \frac{d^2u}{dx^2}=20x^3 \frac{d^3u}{dx^3}=60x^2...
  42. B

    Integration by parts and negatives

    Homework Statement Here are two instances where the negative sign just changes for no reason. The one's all the way on the right. Why? I don't understand what is going on here. For the second one, it should + cos x
  43. B

    More integration by parts

    Homework Statement ∫ x2 sin x Homework Equations uv - ∫ v duThe Attempt at a Solution u = x2 du = 2x dv = sin x v = -cos x step 1. x2 - cos x - ∫ -cos x 2x I think -cos x * 2x becomes -2x cos x so now we have step 2. x2 - cos x - ∫ -2x cos x which means I have to integrate by parts...
  44. B

    Did the author make a mistake in integrating by parts?

    Homework Statement In this video from which there is a screen shot above the author went from x/2 to 2x and all he said was half is two quarters. right a half is two quarters it is not 2. I just want to make sure that he made a mistake because I've been seeing some real bizarre things in...
  45. T

    Parts Per Thousand & Gradients Question

    Hello all I was wondering if anyone could help me with the following:- The equation of a line is Y = -0.00331x + 9907.333. The equation represents distance (x) and elevation (y) The gradient is -0.003311. What is number represents is for every 1 unit I move in the x plane I move...
  46. C

    Repeating integration by parts

    Homework Statement integrate .5e^(t/50)*sin(t) Homework Equations integration by parts uv-∫vduThe Attempt at a Solution I am currently in differential equations and I remember from cal II that I have to keep using the equation above until the integral loops around, then set it equal to...
  47. G

    Cyclical Integration by Parts, going round and round

    Homework Statement Integrate By Parts (i.e. not using formulas) ∫e3xcos(2x)dx The Attempt at a Solution I keep going around in circles, I know at some point I should be able to subtract the original integral across the = and then divide out the coefficient and that's the final...
  48. C

    Building a PC: All Parts Needed & Software to Install

    can all the parts be bought in hardwares? and if anyone has done this can you please give me all the parts needed, also the software you need to install using windows or linux
  49. Fredrik

    F is integrable if and only if its positive and negative parts are

    Homework Statement Problem 2.6.3. in "Foundations of modern analysis", by Avner Friedman. Let f be a measurable function. Prove that f is integrable if and only if f+ and f- are integrable, or if and only if |f| is integrable. Homework Equations Friedman defines "integrable" like this: An...
  50. A

    Slip condition between two parts joined together by shrink-fitting?

    Consider a bearing joint together with a long pipe (with radius a) by using shrink-fitting. The grip between the pipe and the inner ring of the bearing give rise to the surface pressure p at the interface. If a moment M now is applied to the pipe, what will the slip condition between the two...
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