parts Definition and 838 Threads

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. N

    How can substitution make integration by parts easier?

    \int x^3cos(x^2)dx -\frac{1}{2}x^2sin(x^2)+\frac{3}{2}\int xsin(x^2)dx -\frac{1}{2}x^2sin(x^2)+\frac{3}{4}cos(x^2)-\frac{3}{4}\int \frac{cos(x^2)}{x} the last integral
  2. B

    Can Anyone Help Identify These Stepper Motors?

    I have multiple stepper motors i pulled out a printer and I can't seem to find any datasheets on anything. For example one of the motors is made by OKI and it has numbers 3Y25AE1 and QH4-4490. I have looked all over the internet and I can't find anything. If anyone knows a good idea to try it...
  3. T

    Quick question on integration by parts

    Homework Statement I'm following an example in the textbook that states: http://img24.imageshack.us/img24/1672/33686252.jpg I was just wondering what happened to the 2 out the front, I would have been more inclined to think this would be the next step...
  4. P

    How do you know when to use integration by parts on a problem?

    This a techniques of integration question, and I'm wondering how do you know when to use integration by parts on a problem? My book says this bout the Integration by parts procedure. If f(x) is a product of a power of x and transcendental function then we try integration by parts. Can...
  5. G

    Prove Z can be partitioned into 3 parts

    Homework Statement Prove that Z can be partitioned as Z= 3Z \cup (1+3Z) \cup (2+3Z), where m+3Z={m_3n| n\in Z} Homework Equations The Attempt at a Solution Not sure how to start to prove this. I know it has to do with the remainder when an arbitrary integer is divided by 3, but I...
  6. H

    Imaginary parts of roots of unity

    Hi all, What happens when we take the product of the imaginary parts of all the n-roots of unity (excluding 1)? I read somewhere that we get n/(2^(n-1)). How can we prove this? Thanks!
  7. E

    Integration by parts conceptual problem

    1. Suppose : f(1) = 2, f(4) =7 , f'(1)=5, f'(4) = 3 and f"(x) is continuous. Find the value of: \int_{1}^{4} xf''(x)dx Homework Equations IBP formula \int u(x)dv = u(x)v(x) - \int v(x) du The Attempt at a Solution I re-wrote the IBP formula from...
  8. C

    Where Did I Go Wrong in My Integration by Parts Problem?

    Homework Statement Let F(b) be the exact area under the graph of y = x2*e-x between x=0 and x=b for b>0. Find the formula for F(b).Homework Equations int(uv')= uv - int(vdu)The Attempt at a Solution u = x2 and dv = e-x, thus u'=2xdx and v=-e-x. y= -x2*e-x - -2*integral(xe-x). = -x2*e-x...
  9. D

    Conceptual problem with integration by parts.

    Why is it that whenever we encounter a question which can be solved by integration by parts, we get half the function? I mean, suppose a differentiated f(x)g(x) yielded {f'(x) g(x)dx + f(x)g'(x)dx}, then why do we get only {f'(x) g(x)dx} to extract the original function (f(x)g(x)) from?
  10. P

    Why Do I Struggle to Choose the Correct u and dv in Integration by Parts?

    Find http://img214.imageshack.us/img214/4186/problemm.png Homework Equations udv=uv-ƒvduThe Attempt at a Solution lndx=dv (1/X)=v u=x^2+2 du= 2x^2 I looked in the solutions manual and I don't get, why do I keep picking the wrong u & dv?Can someone please show an example on how to pick the...
  11. C

    Integration by Parts: Verify Formula for $\int x^{n} sin x dx$

    Homework Statement \int\frac{t^{2}}{\sqrt{2+3t}} Use integration by parts to verify the formula: \int x^{n} sin x dx = -x^{n} cos x + n\int x^{n-1} cos x dx Homework Equations The Attempt at a Solution For the first one, I attached the picture of my work on paper, as it...
  12. Mentallic

    How can I solve this integration by parts problem for the function x^2/(e^x+1)?

    Homework Statement I=\int{\frac{x^2}{e^x+1}dx} The Attempt at a Solution I tried integration by parts but that didn't work because it just became more complicated in the end. I=x^2ln(e^x+1)-2\int{xln(e^x+1)dx} Then, \int{xln(e^x+1)dx}=xln(e^x+1)-\int{\frac{x}{e^x+1}dx} It...
  13. N

    Cant uderstand some parts this another problem

    here is the problem and solution: http://i30.tinypic.com/2w2mnap.jpg why they divide into two cases? then they find a magnetic field but we don't have any electricity flowing?? the i recognized the formula for a magnetic field from a wire but when we find a the formula from the...
  14. N

    Cant uderstand certain parts this

    here is the question and solution: http://i29.tinypic.com/30cy4cn.jpg i can't understand certain things in here: i can't understand the 3d picture. why the magnetic field in the z direction?? i can't understand how did they find the mutual inductance here. because by this formula...
  15. J

    Integration by Parts of Inverse Tangent

    Homework Statement I must evaluate the indefinite integral: \int x \arctan{x} dx Homework Equations I am using the following format to perform the integration: \int u dv = uv - \int v du The Attempt at a Solution I have tried working the problem substituting x in for u and arctan...
  16. D

    Infinite series by integration by parts

    Hi, I wonder if this hypothesis is true: Let f_n be an arbitrarily chosen n'th anti-derivative of the function f_0. Similarly, let g_n be the n'th derivative of the function g_0. Now, \int^b_a f_0 g_0 \rm{d}x=[f_1g_0]^b_a-\int^b_a f_1g_1 \rm{d}x=[f_1g_0-f_2g_1+...]^b_a+(-1)^n \int^b_a...
  17. D

    Integration By Parts: Need help with a step

    Integration By Parts: Need help with a step... Evaluate the integral: \int ln(2x + 1)dx I worked it out up until: Xln(2x + 1) - \int 2x/(2x + 1) dx Then the next step throws me off. I attached a scan from the solutions manual and circled the part that confused me. Could somebody...
  18. T

    Integration by parts involving partial derivatives

    Homework Statement \int x \frac {\partial f} {\partial x} dx where f=f(x,t) Homework Equations \int u \, dv = uv - \int v \, du The Attempt at a Solution u = x so du = dx and dv = \frac {\partial f} {\partial x} dx so v = \int \frac {\partial f} {\partial x}...
  19. wolram

    Upcycling: Building a Lifters from Salvaged Parts

    What have you built from junk/ stuff laying about your garage or whatever. My next project is to build one of them ( ionic wind) lifters from bits i can find or salvage.
  20. B

    Replacing Brain Cells with Artificial Cells: A Solution for Aging and Mutations?

    Could replacing one or more parts of the cell, using artifical and or/biological material for the replacement(s) possibly make it so mutations did not cause aging in a way where the aging from the mutations is permanent except if/when organ replacements are done. Why/why not. if someone answers...
  21. N

    Integration by Parts with Power Reduction - Confirming Solution

    Homework Statement I(xsin^2x,x) (1/2)I(x(1-cos2x),x) (1/2)I(x,x)-(1/2)I(xcos2x,x) x^2/4-(1/2)I(xcos2x,x) u=x du=dx dv=cos2x v=sin2x/2 x^2/4-xsin2x/4+I(sin2x,x)/4 x^2/4-xsin2x/4-cos2x/8+C book is showing a diffrent solution from integrating by parts before power reduction can somone...
  22. D

    Parts of an 'information' in phyiscs.

    Suppose a physical quantity needs to be represented in pictorial form...for example distance. Such value represented should have 3 parts - 1)Orientation - Or the angle that it makes to the axes of the Cartesian coordinate system under which things are being observed. In the 2 images below...
  23. T

    Use double integrals to show result of integration by parts

    Homework Statement Let F(x) and G(x) be the antiderivatives of f(x) and g(x) on [a,b]. using multiple integration, show that the integral from a to b of f(x)G(x)dx = F(b)G(b)-F(a)G(a) - the integral from a to b of g(y)F(y)dy To do so, consider the double integral of a suitable function...
  24. N

    Integration by Parts: Solving for u and v in cos(2x) and cosx(2x)

    Homework Statement Homework Statement The Attempt at a Solution u= cos(2x) = > du= -2 sin(2x) dv=cosx(2x) =>v= 1/2 sin(2x) ?
  25. S

    Integrating by Parts: Solve e^(-x)cos x dx

    Homework Statement I have attempted and failed solving the following integration: Integrate : e^(-x) cos x dx Homework Equations I tried using the integration by parts rule: uv - (integral) v (du/dx) dx The Attempt at a Solution I let u = e^(-x) and dv/dx = cos x...
  26. D

    Parts of an 'information' in phyiscs.

    From what I think, any physical value has at most 3 parts - 1)Orientation - Or more explicitly, the angle that it makes with axis of the Cartesian coordinate system. Transforming will not change this value. 2) Position - This is the translational stuff...exactly from which point to which...
  27. I

    Integration by Parts: Solving the Integral of Sqrt(x) * ln(x) with Limits 1 to 5

    Homework Statement integral limit 1 to 5 integral of sqrt x * lnx dx a = 1 b= 5 Homework Equations The Attempt at a Solution 2 x (-1 + 2 Log[x]) ------------------ 8 11.99604193 but its not right
  28. M

    Integration by Parts: Int: x*arctan(x) dx

    Because of circumstance (my desire to graduate in 5 years or less), I've been forced to attempt Calc 2 in 2 months time online over the summer. About 75% of it is going smoothly (compared with 105% or so of Calc 1). Homework Statement I'm to solve the indefinite integral: \int x *...
  29. M

    Alternative to Integration by Parts?

    Hey all! I was recently refreshing my memory of integration by parts via some personal reading when I thought, there must be a better way. Integration by parts (while creative in that it integrates the entire product rule) feels very arbitrary to what it's attempting to calculate (at least...
  30. A

    Integration by Parts Problem (Natural Log)

    Homework Statement [Intgrl]ln(x^(2)+4)dxHomework Equations [Intgrl]udv=uv-[Intgrl]vduThe Attempt at a Solution [Intgrl]ln(x^(2)+4)dx, u=ln(x^(2)+4), du=(2x/x^(2)+4), dv=dx, v=x xln(x^(2)+4)-[Intgrl](2x^(2)/(x^(2)+4))dx
  31. G

    How can I integrate by parts this one?

    Homework Statement I have to solve the following integral 1/(sqrt[x] * ln[x]) from 2 to infinity Homework Equations The Attempt at a Solution u= ln[x] dv=1/sqrt(x) du= 1/x v= 2 sqrt(x) If I do this I get lim (ln b/ sqrt[x] - 4 sqrt[x] -...
  32. B

    Probability of faulty parts shipped. Tough question

    Okay, I am doing some revision questions for probability and this question has me stuck.. I've spent hours on this one problem and i can't get my head around it. I have the answers to it, but they don't show the working. So here goes.. Question: A supplier has shipped a lot of 6 parts to a...
  33. E

    Specific parts of the emission spectrum of a sodium lamp

    Homework Statement Part a) The emission spectrum for Sodium lamp contains a reasonably bright red line in its spectrum. What is its origin? Part b) The possible transitions between electron energy levels for Sodium were analysed. There were no transitions between the s series (s subshell)...
  34. A

    Integration by Parts: Find Integrals | 65 Characters

    Formula for integration by parts: \int f(x)dx = \int u dv = uv - \int v du Use integration by parts to find the following integrals: a) \int x e^{1-x} dx b) \int_1^4 \frac {ln \sqrt x} {\sqrt x} dx c) \int_{-2}^1 (2x+1)(x+3)^{3/2} dx d) \int x^3 \sqrt{3x^2+2} dx Answers in back of the...
  35. F

    Integration by Parts of x^5cos(x^3)

    Homework Statement \int x^5cos(x^3) dx Homework Equations \int uv' = uv - \int u'v The Attempt at a Solution \int x^5cos(x^3) dx \frac{(x^5)*(sin(x^3)}{(3x^2)} - \int\frac{5x^4*sin(x^3)}{(3x^2)} dx \frac{(x^3)*sin(x^3)}{3} - \int\frac{(5x^2)*sin(x^3)}{(3)} dx...
  36. Y

    Why Separate x^7 into x^4 x^3 in Integration by Parts?

    I have a couple questions about a certain problem on http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/intbypartssoldirectory/IntByPartsSol3.html#SOLUTION%2016 On number 18... 1) What is the logic behind separating x^7 into x^4 x^3 2) In the translation from dv to v, how did x^3...
  37. A

    Integration by Parts: Q6 - (-(0-0)), Q3 Explained

    Homework Statement In question 6, where does the -(0-0) part come from. The instructor did this for another question, question number 3 as well except in the other question the resulting value was a non-zero one and thus affected the answer.. any help appericiated...
  38. C

    Integration by Parts of a Double Integral

    Homework Statement ∫∫xy(x^2+y^2)^(1/2)dydx over the range 0 to 1 for both x and y. Homework Equations I believe that it requires integration by parts. Any help would be greatly appreciated.
  39. J

    Improper Integrals with u sub and integration by parts ?

    Homework Statement The integral from 1 to infinity of (lnx)/(x) dx Homework Equations U substitution and integration by parts The Attempt at a Solution Cant decide what to use as my "u" . . can anyone help with this part ? -Jay J-
  40. L

    Integration by parts x5(lnx)2 dx

    Homework Statement Integrate the following: (Ill use { as the integration sign) {x5(lnx)2 dx Homework Equations {u dv = uv - {v du I'm really new to integration by parts, and unfortunately I am having to learn it out of a book for now. I sort of get the idea, but this one just doesn't look...
  41. A

    Integration by parts [ x^3 * sqrt (1 - x^2)

    I have tried pretty much every method I can think of to solve this integral but I haven't managed to get much luck. I used a derivative value (U) of x^3 and managed to get a x^5 term inside the next part and there is no easy way to get a derivative for the square root of 1-x^2. I tried...
  42. S

    What is the value of this term and why is it not included in the given passage?

    I found this passage in a book: http://img8.imageshack.us/img8/1452/75717730.jpg where Φ(x) is the c.d.f. of the normal distribution. However, using integration by parts I also get this term which is not included in the passage: [ e^{itx} \phi(x) ]^{+ \infty}_{- \infty} where i is the...
  43. A

    Is Integration by parts the only way?

    When faced with an integral which contains the product of two functions, must you always default to integration by parts? Is there no alternative method? Perhaps, one intended for more complex functions? Thank you.
  44. A

    Solve Integration by Parts Questions: Part I & II

    I am stuck with 2 questions. 1. http://132.239.150.164/math/img/math_967.5_fabcf8ac5b3f2459050993af33426844.png[/URL] 2. http://132.239.150.164/math/img/math_972_41ec111060693034ac0775fd52778392.png[/URL] Homework Equations...
  45. N

    Help with integration (1) involving integration by parts etc

    Homework Statement Solve for indefinite integral of (7x^3)/sqr(4+x^2)(dx) Homework Equations I just can't seem to find the right solution. The Attempt at a Solution First of all, we can just factor the 7 out of the integral for now since it is only a constant. the inverse square...
  46. K

    Integration by parts and substitution help

    Integration by parts and substitution help! Homework Statement ∫0 -1 e ^√x+1 Homework Equations The Attempt at a Solution
  47. I

    Int sec x / tan^2 do i do this by parts?

    int sec x / tan^2 do i do this by parts?
  48. J

    Integrating sin(x)/x using Integration by Parts

    i'm having troubles to integrate \int\frac{sin x}{x} dx could anyone help me with hints? i tried using integration by parts, but i see it as a never ending chain, sin will change to cos... and x^-1 will become -x^-2 and so on
  49. C

    Integration by parts with trig function insanity

    Homework Statement Let In=the integral from 0 to pi/2 of sinnxdx show that (I2n+1)/(I2n)=(2n+1)/(2n+2) Homework Equations integral from 0 to pi/2 of sin2n=(2n-1)pi/4n The Attempt at a Solution I can't write down all that I've done because it's just too ridiculous. I've tried lots...
  50. L

    Integration by Parts: Solving x^2(cosx)dx with Step-by-Step Guide

    Homework Statement solve by using intergration by parts x^2(cosx)dx Homework Equations My question is i got this answer but my computer algebra system gave me this answer (x^2-2)sin(x)+2xcos(x) can you tell me where i went wrong?? The Attempt at a Solution u=X^2 dv=cosx du=dx...
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