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. T

    Reduction formula question (int by parts)

    Homework Statement Let I_{n} = \int^{2}_{0} x^{n}e^{x} dx where n is a positive integer. Use integration by parts to show that 2^{n}e^{2} - nI_{n-1} By first finding I_{1} = \int ^{2}_{0} xe^{x} dx find I2 and I3.Homework Equations I'm sure your all aware of the formula for Int by...
  2. T

    Tricky integration by parts question

    Homework Statement Find \int^{1}_{0} (x^{2} - 3x + 1)e^{x} dxHomework Equations Let f =(x^{2} - 3x + 1) [tex g = e^{x}[/tex] f' = 2x - 3 \int (g) dx = e^{x} The Attempt at a Solution We are going to have to use intergation by parts twice as the degree of the first function (f) is 2...
  3. P

    Distributions and Intergration by Parts

    "Distributions" and Intergration by Parts Homework Statement Has it been proven that it is ok to use Integration by parts on "Distributions" like Dirac Delta functions inside an integration? Homework Equations Need to figure out how to write integral signs and Greek alphabet symbols...
  4. 0

    Integration by Parts evaluation help

    Hi, Can you tell me if I am on the right track with this problem. Thanks in advance. Homework Statement Evaluate the integral using integration by parts Homework Equations ln(2x + 1)dx The Attempt at a Solution ln(2x + 1)dx = ln(2x + 1) * 1dx Let U = ln(2x + 1)...
  5. D

    Integration by parts homework help

    \int_0^{infinity} \ e^{-s*t}*t*cos(t) dt I tried integration by parts with u=t*cost and dv=e^(-s*t) but that didn't get anywhere. I then tried: \L{t^n*g(t)}=(-1)^n d/ds[\int_0^{infinity} \ e^{-s*t}*cos(t) dt but again nothing was working. This is a Laplace Transformation where ft=t cos(t)
  6. M

    Integration By Parts: Solving int.arctan(2x)dx for Calculus Homework

    Integration By Parts? Homework Statement int.arctan(2x)dx Homework Equations Integration By Parts The Attempt at a Solution In the attached image is the original problem with the ansewer I came up with using integration by parts and then a v=sub. later in the problem I did not...
  7. S

    Difficulty With Integration by Parts

    Homework Statement Homework Equations The Attempt at a Solution What I am unsure of is how to find the derivative of u. Since the original integral is integrating with respect to y, should I be finding the derivative of u with respect to y, and treat the x's as contants?
  8. S

    Solving Integration by Parts with a Reduction Formula

    Homework Statement Use integration by parts to prove the reduction formula: http://img214.imageshack.us/img214/1234/24206074.jpg Homework Equations The Attempt at a Solution what confuses me about this question is that its not in the form sqrt(a2 + x2) but its in ^n instead of...
  9. T

    Integration by Parts: Struggling with Homework

    Homework Statement Here is a question I'm struggling with. I encountered it in a paper, and although a solution is provided I'm not so sure I understand where they're coming from. Homework Equations \int_{r_1}^{r_2} \overline{v}\frac{1}{r}\frac{d}{dr}(r\frac{du}{dr})rdr where...
  10. C

    Integration by parts help just the beginning part for this one

    Homework Statement intergral from pi to 0. of (sin(3t)dt)^4 The Attempt at a Solution okay so i know how to do this but when i tried substitution putting 3t=u and (1/3)du= dt i always came with the the wrong coefficient at the end with the answer and so i would multiply it...
  11. M

    Parts, componets, and things that do stuff

    Parts, componets, and things that "do stuff" Hi guys! I'm actually an electrical engineering student, but I figured this might be more applicable here. I'm trying to find websites that are good for ordering parts such as bearings, shafts, gears, chains, cogs, and more. I'm planning on...
  12. C

    Integrating by Parts: tan-1x dx

    Homework Statement integral tan-1x dx i am supposed to integrate this by parts Homework Equations The Attempt at a Solution integral tan-1x dx = integral cosx/sinx dx u=cos x, du=-sin x dx v=ln sin x, dv= sin-1x dx integral cosx/sinx dx= cosx ln(sinx) - integral[ ln(sinx)(-sinx) dx] is...
  13. T

    Integration by Parts - Choice of variables

    Homework Statement I'm getting different results when choosing my u & dv for Integration by Parts on the following integral: \int 2x^3 e^x^2 dx (Note, the exponent on 'e' is x^2) This yields the correct solution: u = x^2 dv = 2x e^x^2 dx du = 2xdx v = e^x^2 However, I have tried using...
  14. A

    Integration by Parts with sin and ln(x)

    Homework Statement The method to use to integrate the function is up to us. The choices are: 1) U-substitution 2)Integration by Parts 3)Trigonometric integrals 4)Trigonometric substitution 5)Partial fraction Homework Equations According to me, the best way to do it is to use...
  15. S

    Integration By Parts: Volume - help

    Homework Statement Use the method of cylindrical shells to find the volume generated by rotating the region R bounded by the curves y=e1.6 x, y=e−1.6 x and x=0.6 about the y-axis. Homework Equations V=$\displaystyle \Large \int _a^c 2pix (yt - yb) dx$ The Attempt at a Solution...
  16. S

    How Do You Solve Integrals Using Integration By Parts?

    Homework Statement 1.$\int x^ne^xdx$ 2.$\int \sin ^nxdx$ Homework Equations $ \displaystyle \Large \int fg dx = fg - \int gf' dx$ The Attempt at a Solution 1. f=xn g'=ex g=ex f'=nxn-1 then just plug it in the formula? i tried but i don't get the right answer.. 2. i have...
  17. 3

    What is the Integration by Parts Method for Solving Integrals?

    Homework Statement \int\frac{x^3}{\sqrt{1-x^2}}dx I have to use integration by parts on the above integral. Homework Equations The Attempt at a Solution u=x^3 du=3x^2dx dv=\frac{1}{\sqrt{1-x^2}}dx v=arcsin (x) =x^3arcsin (x)-3\int\ x^2arcsin (x)dx u=arcsin (x)...
  18. G

    Software for designing parts of a jet

    Hello, I'd like to say hi to everyone since I'm pretty new here, and I guess my first post goes directly to asking a question. Anyway, could someone here recommend me some program for designing parts of a jet or a space vehicle that resembles a delta winged jet. I'm doing this for learning...
  19. P

    Real and imaginary parts of an expression

    can anyone tell me how to get the real and imaginary parts of the following function : (x+ i y)* Log( a+i b) where x, y a and b are all real numbers and i =sqrt (-1). Thanks very much
  20. R

    Indefinite Integral - By parts works right?

    Nevermind, it's late and I realized why it doesn't work because I forgot to take into consideration that the denominator is (1/polynomial) Anyone care to explain to me how to do it the proper way? 1. Question 1 \int (x+2)/(x²+x+1) dx The only reason I ask is because my teacher...
  21. M

    Calculate forces and size parts in a steering arrangement

    Homework Statement I am trying to size parts of a boat, but I don't believe in my results. An attempt to solve one subproblem of this in a rulebook based way can be read here: http://www.boatdesign.net/forums/boat-design/rudder-scantling-31263.html Is it appropriate to bring that question...
  22. A

    Integration by parts of a function

    the function is c = 15te-.2t the goal is to integrate it from t = 0 to t = 3 so to set up the integral i took out the 15 first so i got: 15 * integral from 0 to 3 of t*e-.2t i set u = t and so du = dt dv = e-.2tdt so v= -5e-.2t so following the integration by parts formula i got...
  23. A

    Integrate xarctan(x^2)dx: Steps & Solution

    the problem is find the integral of xarctan(x^2)dx i set w = x^2, so 1/2dw = xdx then i plug that into the integral to get the integral of 1/2arctan(w)dw so i let u = arctan(w) and dv = dw so du = dw/(1+w^2) and v = w so then the integral of udv = uv - integral of vdu so...
  24. R

    Integration by Parts substitution

    Homework Statement \int\arctan(4t)dt Homework Equations The Attempt at a Solution \int\arctan(4t)dt = t\arctan(4t) -4 \int \frac{t}{1+16t^2}dt I'm stuck at this point. I think I need to make a substitution for the denominator, but I'm not sure how to go about doing so.
  25. R

    Simple integration by parts problem

    Homework Statement \int \ln(2x+1)dx Homework EquationsThe Attempt at a Solution u = \ln (2x +1) du = \frac{2}{2x+1} dv = dx v = x xln(2x+1) - \int \frac {2x}{2x+1}dx I'm not sure how to proceed. Do I separate the fraction in the integrand or do long division? I think I separate the...
  26. Z

    Integration by Parts: Solving \int \frac{x^3e^{x^2}}{(x^2+1)^2}

    Homework Statement \int \frac{x^3e^{x^2}}{(x^2+1)^2} The Attempt at a Solution Well, this problem is hard, so I thought to use u = x3ex2 so du = x2ex2(3+2x2) dx and dv = (x2+1)-2 then v = -2(x2+1)-1 Please check v though to make sure my algebra is right. so then using the by parts formula...
  27. E

    Integration by parts, can you do this?

    I've seen this formula stated and used, ( in a stanford university video lecture) \int \frac{dA}{dt}B\ dt = - \int \frac{dB}{dt}A\ dt with the condition that you don't vary the end points. but i don't understand how you can just remove the AB term from the right hand side, and I've...
  28. G

    Integrate by Parts: Solving \int \ln (x^2 + 1) \, dx

    Homework Statement Find or evaluate the integral using substitution first, then using integration by parts. \int \ln (x^2 + 1) \, dx The Attempt at a Solution Let \: u = x^2 + 1 du = 2x \, dx dx = \pm \frac{du}{2 \sqrt{u - 1}} Then \int \ln (x^2 + 1) \, dx = \pm...
  29. M

    Area of the region bounded between two curves with integration by parts

    Homework Statement Find the area bounded between the two curves y=34ln(x) and y=xln(x) Homework Equations Integration by parts: \intudv= uv-\intvdu The Attempt at a Solution First I found the intersection points of the two equation to set the upper and lower bounds. The lower...
  30. C

    Integration by Parts separately

    Homework Statement Integrate: -\frac{2}{\theta} \int^{\infty}_0 y e^{-2y/\theta} dy + \frac{2}{\theta} \int^{\infty}_0 y e^{-y/\theta}dy Homework Equations The Attempt at a Solution Let u = y/theta; y=u*theta; dy = du*theta, which becomes -2 \int^{\infty}_0 u \theta e^{-2u}...
  31. L

    Laplace transform: function defined by parts

    I have this DE: \[y'' - 4y' + 8y = f(t) = \left\{ \begin{array}{l} t{\rm{ }},t \in [0,2) \\ t + 1{\rm{ }},t \in [2,4) \\ 0{\rm{ }},t \ge 4 \\ \end{array} \right.\] I have problems transforming f(t). I know that when I have a function defined by parts, I...
  32. J

    In two equal complex numbers, what parts are equal to each other?

    When there are, say, two complex numbers that are equal. What can we say about their equality? Can we say that the real part of one is equal to the real part of the other? Similarly, can we say that the complex part of one is equal to the complex part of the other? Is this what it means when...
  33. D

    Can we use integration by parts for improper integrals?

    What's up with this \int_{-\infty}^\infty \sin{x}\frac{1}{x}dx=\pi Now I try integration by parts \int_{-\infty}^\infty \sin{x}\frac{1}{x}dx=[-\cos{x}\frac{1}{x}]_{-\infty}^\infty-\int_{-\infty}^\infty \cos{x}\frac{1}{x^2}dx = -\int_{-\infty}^\infty \cos{x}\frac{1}{x^2}dx = \infty...
  34. T

    Summation by Parts: Lim x->1 (1-x)f(x)=L

    Homework Statement Let lim n-> ∞ a_n = L. Then, let f(x) = ∑ from n=0 to ∞ of (a_n)(x^n). Show that the lim x-> 1 (1-x)f(x) = L. Homework Equations The Attempt at a Solution This one is pretty far over my head. I know at some point you're supposed to use Abel/SBP, but here is what I have so...
  35. S

    Real and imaginary parts of wave function

    A very general question: What do the real and imaginary parts of a wave function correspond to physically? Cheers
  36. D

    Understanding Wave Displacement: Frequency, Wavelength, and Speed Calculation

    The displacement of a wave traveling in the positive x-direction is y(x,t) = (3.5 cm)cos(2.7x - 124t), where x is in m and t is in sec. What are the (a) frequency, (b) wavelength (in m), and (c) speed (in m/s) of this wave? I don't know how to do this problem at all. I could use some help...
  37. R

    Summation of a sequence by parts.

    I hope can someone clarify this for me. I have a sequence f(of n) which is like this: fn(x) = 0-- if--x<\frac{1}{n+1} is = sin^2(x/pi)--if--\frac{1}{n+1}<=x<=\frac{ 1}{n} is = 0--if--\frac{1}{n}<x (the - are for spaces because I don't know how to do it. Nothing is negative) Then...
  38. A

    Integrate e^(-theta)cos(2theta): Get Help Now!

    Homework Statement Evaluate the integral (e^-theta) cos(2theta) I got this as my answer e^(-theta)-sin(2theta)+cos(2theta)e^(-theta)+C But it was wrong All help is appreciated.
  39. G

    Integration by Parts guidelines

    I've been trying to find this online, but I haven't been able to find any site that really explains it: when performing integration by parts, is there some rule or set of guidelines to determine which part of the equation is u and which is dv?
  40. M

    HELPSubstitution and Integral by Parts

    I'm having big trouble when trying to figure this integral out. Please help! Integral (from 0 to infinity): ((x^2)/a)*e^[(-x^2)/2a] dx a is a constantThanks in advance!
  41. M

    Solve Integral Using Integration by Parts

    Hello :smile: I was hoping someone could help me with this integral. Homework Statement I=\int{(x^2sin(5x^3-3))}dx Homework Equations \int{(u.\frac{dv}{dx})}dx=[uv]-\int{(v.\frac{du}{dx})}dx \frac{dy}{dx}=\frac{dy}{du}.\frac{du}{dx} 3a. The first attempt at a solution...
  42. N

    Parametric Equations with Trig sub and int by parts

    Homework Statement x=cos^2(t) y=cos(t) (a) Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. (b) What is the length of the curve? Homework Equations Length of an Arc: integral of alpha to beta sqrt((dx/dt)^2+(dy/dt)^2) The...
  43. P

    How is the freezer part of a refrigerator is more cooler than the other parts?

    please explain me..
  44. X

    Integration by parts involving exponentials and logarithms

    Homework Statement Using integration by parts, integrate: (1/x^2)(lnx) dx with the limits e and 1 Homework Equations [uv]to the limits a b - the integral of (v)(du/dx) dx (sorry, don't know how to write out equations properly on a computer) The Attempt at a Solution I've...
  45. Ivan Seeking

    CNN parts company with their crackpot, Lou Dobbs

    I think this is great for CNN. Dobbs was not a respectable journalist. http://www.ajc.com/business/grand-exit-for-cnns-197683.html?cxtype=rss_news_128746 Like so many pseudo-journalists on TV these days, Dobbs and his show were loaded with bias. Just check any poll of his to see how...
  46. S

    Partial pressure of gases in various parts of the respiratory system

    Hello everyone, Ok to understand the respiratory system, proper understanding of this diagram is essential. Something I don't have, so if anyone can help me with these questions I would be very greatful. Thanks :smile: http://img515.imageshack.us/img515/8923/rightbv.jpg 1. Anatomic dead...
  47. H

    Current in a Resistor network ( 2 parts of part b)

    Homework Statement Consider the resistor network shown in the figure below, where R1= 5\Omega and R2= 7\Omega . (a) Find the equivalent resistance between points a and b Req=([1/6 +1/5]+7)+12+6=(9.73)-1+18-1=6.32\Omega (b) If the potential drop between a and b is 12 V, find the...
  48. P

    Parts of a cigarette lighter

    was just curious to know what a cigarette lighter made of what metal they use in the exterior where the light comes out.what kind of plastic is used to hold the liquid?will the metal melt off if its switched on for a while? what's the difference between a $1 lighter and the $24 zippo lighter ...
  49. M

    Imaginary parts of GAMMA(1/2+I*y)

    Hi: Does anyone know of an explicit formula for the Real and Imaginary parts of GAMMA(1/2+I*y) as functions of y ? I know about |GAMMA(1/2+I*y)|^2 =Re(GAMMA(1/2+I*y))^2+Im(GAMMA(1/2+I*y))^2= Pi/cosh(Pi*y) but can't find anything about each of the Real and Imaginary terms...
  50. P

    Name for integration by parts shortcut

    Hi all. I've recently learned a shortcut for integration by parts, but don't know what it's called or where it comes from. The trick is to find \lambda such that f'' = \lambda f and \mu such that g'' = \mu g, providing both are constants and \lambda\neq\mu. Then \intf(x)g(x)dx =...
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