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. U

    Integrating by Parts: Solving for Probability in Sphere of Radius a0

    Homework Statement Given that the probability of finding a 1s electron in a region between r and r + dr is: P = \frac{4}{a_{0}^{3}}r^{2}e-2r/a0dr work out the probability that an electron would be found within a sphere of radius: i) a0 Homework Equations The Attempt at a...
  2. R

    How can I use integration by parts to solve this indefinite integral?

    Homework Statement Indefinite Integral (x^3)(e^x) Homework Equations The Attempt at a Solution I know I need to substitute t=x^2 t^(3/2)e^sqrt(t) U=e^sqrt(t) du=e^sqrt(t) dt dv=t^(3/2) V= (5/2)t^(5/2) Because it has an exponential function, I know I need to use the...
  3. K

    Easy integration by parts question.

    Homework Statement Hi This is something i don't remember what I'm supposed to do. So anyway here goes. For example if my function was xe^yx and i wanted to integrate with respect to dx then i do an integration by parts with these variables: u = x dv = e^yx now my question...
  4. D

    Evaluating Integral using Parts

    Pardon my use of the program! I am new to Physics Forums! Homework Statement EVALUATE The Integral of: Square root of (x^2 + 2x) The Integral of: x * Square root of (x^2 + 7) Homework Equations Integrating by Parts Method The Integral of udv = u*v - the integral of v*duThe Attempt at a...
  5. G

    Parts of a cuboid after n cuts

    Homework Statement I have been asked to find a recursive formula for the number of parts of a cuboid after n cuts, and then prove my formula. The Attempt at a Solution I have through a 3D drawing program figured out a the number of parts after 8 cuts cuts, parts 1,2 2,4 3,8 4,15...
  6. S

    How to built Carbon Fibre parts at home

    How Can i built carbon fibre parts at home work shop?
  7. T

    Where to Find Cheap Miniature Pumps & Solenoid Valves

    I'm trying to start a project that uses miniature parts, solenoid valves and pumps mainly. It is very hard if not impossible to find these parts. I did manage to locate some parts that are seemed suitable for my needs. But, these parts are from some wholesale distributor. What I would like to...
  8. P

    Integral involving parts and trig sub

    integral of xarcsinx dx integration by parts and a trig sub by parts I get (x^2)/2 arcsinx - integral (x^2)/sqrt(1-x^2) after that trig sub and i get integral of sin^2 then I used the double angle identity so integral of 1/2 - the integral of (cos2)/2 so i get 1/2...
  9. N

    How Do You Solve Integral of e^(2y)sin(2y) dy Using Integration by Parts?

    Homework Statement Evaluate integral of e2ysin(2y)dy using integration by parts.Homework Equations integral udv = uv - integral vdu The Attempt at a Solution I tried applying the above equation several times, but the integral and derivative of both e2y and sin(2y) will always have a y in...
  10. B

    Integral of x^3 e^(x^2)/(x^2+1)^2

    how would i go about finding the definite integral of this (x^3*e^(x^2))/(x^2+1)^2
  11. G

    Several integration by parts problems

    Homework Statement a. integral of x arcsec(x) dx b. integral of sin(root x) dx *Instruction says that I should use substitution before integration by parts. c. integral of 2x^3 cos(x^2) dx *Instruction says that I should use substitution before integration by parts. Homework...
  12. K

    Integrals By Parts With Infinity As Limit

    \int_0^\infty \lambda x e^{-\lambda x} dx How do I use the limits (infinity and 0) after getting the equation from integration by parts?
  13. L

    Physical meaning of parts of electromagnetic wave

    in E = E_0exp i(k dot r - wt) or E = cos(k dot r - wt) what does k dot r physically represent? Can r be any position in space or must it lie on the wave? (I physically understand what a dot product is)
  14. F

    Why is the integration constant excluded when finding v in integration by parts?

    We know the formula is \inline{\int udv=uv-\int vdu} but when you say that for example, dv=e^x dx, then why when you integrate to get v, you don't include the integration constant? For this integral: \int xe^{x}dx dv = e^x dx v = e^x + C?
  15. M

    Solve Integration by Parts: Arctan(4t)

    Homework Statement \int arctan(4t) Homework Equations I know what the answer is to the problem but when i look at the solution i have no idea how they get from one step to the next. The Attempt at a Solution once we integrate by parts we get 1/4 U arctan(U) - 1/4 \int U/1+U^2...
  16. M

    Easy integration by parts help

    Homework Statement integral of ln(2x +1) Homework Equations I know this is an easy problem but i can not seem to figure out what to substitute for my U and my dV. I was thinking on making my U= 2x+ 1. but then my problem is what would my dV be? ln U? lnx? the ln is throwing me off a bit...
  17. W

    Evaluate using Integration by parts

    Homework Statement If g(1)=3, g(5)=8 and the integral from 1 to 5 of g(x)dx=-9. Then, evaluate the integral from 1 to 5 of xg'(x)dx. 2. Homework Equations and attempt at solution I used integration by parts to get =xg(x)-(integral of)g(x)dx from 1 to 5. Then substituting in, I get...
  18. D

    Integrating 1/xln(x) using integration by parts

    Homework Statement Integrating 1/xlnx by parts... Homework Equations Find the integral of 1/xlnx The question asks to solve by substitution, which I can do and results in ln(ln(x)) + c It then asks to compute using integration by parts, and then to explain how it can be true (because...
  19. K

    What Are the Velocities of the Broken Parts in a Plane Explosion?

    Homework Statement A plane of a mass 5000 kg moving horizontally in 150 m/s break into two parts 2000 kg and 3000 kg because of a internal explosion. If the bigger part be thrown away with a 400 m/s relative to other part to opposite direction of previous moved direction before explosion...
  20. M

    Solve Integration by Parts Homework: Find Error

    Homework Statement [/b] http://i324.photobucket.com/albums/k327/ProtoGirlEXE/Capture1.jpg The attempt at a solution[/b] http://i324.photobucket.com/albums/k327/ProtoGirlEXE/100_0635.jpg Answer I got: http://i324.photobucket.com/albums/k327/ProtoGirlEXE/Capture2.jpg I thought my...
  21. T

    How Can Integration by Parts Be Applied to Solve Advanced Calculus Problems?

    Homework Statement Integrate the following by parts twice \int_{a}^{b}\frac{d}{dr}(r\frac{dT(r)}{dr})\psi(r)dr and show that it can be written as -\lambda^2\bar{T} , where \bar{T}=\int_{a}^{b}r\psi(r)T(r)dr and the function \psi satisfies the following equation...
  22. A

    Volume of Revolution/Integration by Parts problem

    Homework Statement Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y=e^x and the line x=ln13 about the line x=ln13. Homework Equations The Attempt at a Solution I'm not really sure as to how to do...
  23. F

    Integration by parts difficulties

    Just working through a problem Acheson's book (From Calculus to Chaos) if anyone knows it.. eq 8.6 in this book.. As he's working through the problem he makes the step of this: m\int_{t_{1} }^{t_{2}} \left( \dot{y}_{\scriptscriptstyle A }\dot{\eta} - g\eta \right)\,dt (1) to...
  24. F

    Number of partitions of 2N into N parts

    The number of partitions of an even number 2N into N parts appears to be equal to the number of partitions of N. Is this known? If so: Can anyone provide a reference of the corresponding proof? Thanks in advance for any information on this.
  25. M

    ATH 101: Integration by Parts - Exponential Distribution

    Integration by parts - Exponential distribution Homework Statement Solve the following definite integral: \int^{\infty}_{0} \frac{1}{\lambda} x e^{-\frac{x}{\lambda}} dx I'm asked to solve this integral. The solution is \lambda, although I'm not sure how this was done. Homework...
  26. T

    Problems with integration by parts

    Homework Statement Hi all! I seem to be having trouble doing integration by parts. I seem to have a pretty clear picture of the steps I need to do but something seems to always trick me. Usually I would ask my prof but she is away for a week. I use the formula: uv - ∫vdu = given...
  27. FeDeX_LaTeX

    Solving Difference Equations with Homogeneous and Inhomogeneous Parts?

    Hello; This is not a homework question, but something I was wondering about solving difference equations. For example, how would I solve the following difference equation; F_{n} = 2F_{n - 2p + 5} + 6p - 17; n, p \in \mathbb N Since it has homogeneous and inhomogeneous parts together (and two...
  28. T

    Proof of Integer Parts of Real numbers

    I am struggling to understand the proof for integer parts of real numbers. I have used to mean less than or equal to because I could not work out how to type it in. I need to show that: ∃ unique n ∈ Z s.t. nx<n+1 The proof given is the following: Let A={k∈Z : kx} This is a...
  29. M

    Cathode Rays Experiment some missunderstood parts

    Hi all I don't know If this is the suitable section for this post.. but at all.. let's see if anybody can make me understand this :):) You all know of course J.J. Thomsons's three CRT experiments... The first one was aiming to prove that the appearing rays and the negative charges...
  30. B

    Integrating e^x(x+1)lnx Using Integration by Parts

    \[\int e^x(x+1)\ln x \ dx \] Not sure how to approach this. Would I have to multiply it out first?
  31. S

    Integration By Parts VS U-Substitution

    The past few examples in my review book demonstrated u-substitution to integrate trig functions. The example I'm on suddenly shows integration by parts. The book doesn't explain why this method is used over u-sub. \intsec3x dx In what situation am I supposed to use one method over the other?
  32. J

    Double integrals that involve integration by parts

    Homework Statement Evaluate the double integral. Homework Equations integral by part: uv - integral of v*du The Attempt at a Solution I wrote out my works. And I am just stuck at the x integration... Please click on the links to see the pictures. I don't want to resize it which may...
  33. Telemachus

    Solve Integral with Integration by Parts: 3xcos(x/2)dx

    Homework Statement Hi there. I'm confused about this exercise. It asks me to solve the integral using integration by parts. And the integral is: \displaystyle\int_{}^{}3x\cos(\displaystyle\frac{x}{2})dx The Attempt at a Solution What I did: u=3x du=3dx dv=cos(\displaystyle\frac{x}{2})...
  34. T

    Solve Summation by Parts for Sum[n/3^n]

    Homework Statement Using summation by parts, find Sum[n/3^n]. Homework Equations Sum[a_k*b_k] = s_n*b_(n+1) - Sum[s_k(b_(k+1)-b_k] The Attempt at a Solution Let a_k = 1/3^k and b_k = k. Then b_(k+1)-b_k = 1. But what is s_k? I know that it is 1/3 + 1/3^2 + 1/3^3 + ... but...
  35. estro

    Conditional Convergence and the Comparison Test: A Proof by Contradiction

    Series convergence "by Parts Supose: \sum c_n = \sum (a_n+b_n) (*1) \sum a_n is conditionaly convergent (*2) \sum b_n is absolutly convergent (*3) And I have seen this proof: [Proving \sum c_n is conditionally convergent] From (*1) and (*2) \Rightarrow \sum c_n its...
  36. J

    Are conserved the spin and orbital parts of the angular momentum?

    ¿Are conserved the spin and orbital parts of the angular momentum? For example , we have a particle decay into two photons, and you want to see if the angular momentum is conserved: J(total angular momentum)=S(spin)+L(orbital) The question is: -¿only total J is conserved? (and s or l...
  37. M

    Integration by Parts: Solving Indefinite Integral (x+3)/(x^2+6x) dx

    Homework Statement Evaluate the indefinite integral. ∫(x + 3)/(x^2+6x) dx Homework Equations This is an online homework prob. that covers sections integration by parts and substitution in indefinite integrals. it looks to me that it fits into the formula ∫udv=uv-∫vdu if you change...
  38. G

    Integrating by parts in path integral (Zee)

    Hi all, I have an exceptionally basic question, taken from P21 of Zee. Eq. 14 is Z=\int D\psi e^{i\int d^4x(\frac{1}{2}[(\partial\psi )^2-m^2\psi^2] + J\psi)} The statement is then made that 'Integrating by parts under the \int d^4x' leads to Eq. 15: Z=\int D\psi e^{i\int...
  39. stripes

    Integration by Parts: Where Did I Go Wrong?

    Homework Statement Gosh I've been asking a lot of questions lately...anyways... I tried this question two separate times and couldn't manage to figure out where i went wrong... \int e^{-x}cos2x dx Homework Equations uv - \int v du = \int u dvdx The Attempt at a Solution let u = e^{-x}...
  40. S

    Converting parts per million (ppm) and mol of ions

    1. Fluorine compounds are added to water, the concentration being 0.90 ppm. a. What amount of fluoride present 1.0g of water? Solution- (just need to know what the number mean) Divided 0.90 pm by 1,000,000, which I assume is the grams of substance per kilogram? Then divided that...
  41. R

    Curious Question; find ⌠cotx using integration by parts

    Homework Statement find ⌠cotx using integration by parts with using u= 1/sinx and dv= cosx Homework Equations cotx=cosx/sinx The Attempt at a Solution u= 1/sinx and dv= cosx dx du = -cotxcscx dx v= sinx ⌠udv = 1 + ⌠sinx cotx cscx sinx and cscx cancel out. ⌠cotx = 1 +...
  42. B

    Tabular Integration by Parts Repeated

    So, in my class we are learning how to use the tabular method to solve an integration by parts problem... but what happens if the two parts of the integral continuously repeat? The example I have in mind is \int e^x sin(x) dx. I know how to solve this using repeated integration by parts...
  43. T

    Integrating by Parts: Showing $\int \frac{1}{1-x^2}dx$

    Homework Statement By integrating by parts , show that \int \frac{1}{1-x^2}dx=\frac{x}{1-x^2}-\int \frac{2x^2}{(1-x^2)^2}dx Homework Equations The Attempt at a Solution I don see which is u and v.
  44. L

    Integration by parts homework problem

    How do I integrate the following: \int_0^\infty r e^{-ar} \sin{(Kr)} dr i tried writing r e^{-ar} = -\frac{d}{da} e^{-ar} and using integration by parts but i couldn't get anywhere. any ideas?
  45. M

    How Do I Solve ∫e^-x cos(2x)dx Using Integration by Parts?

    Homework Statement ∫e^-x cos(2x)dx Homework Equations I'm trying integration by parts and I set u=e^-x and dv=cos(2x) The Attempt at a Solution I got to where ∫udv= (e^-x)(1/2 sin(2x))+1/2∫sin(2x)e^-x I am trying to run through a second time and I'm a little stuck
  46. M

    U substitution or substitution by parts?

    Homework Statement ∫〖e^√x/√x dx〗 would this be a u substitution or a substitution by parts? Homework Equations The Attempt at a Solution
  47. B

    Problem with integration by parts

    Homework Statement the question : integrate the following : integration of d(y/x) = integration of(c cos x/x^2) dx , where c is a constant Homework Equations integration of d(y/x) = integration of(c cos x/x^2) dx y/x = c integration of (c cos x/x^2) dx (*) = c(x^-2...
  48. N

    Integration by parts (LIPET Or LIATE)

    Homework Statement Can anyone tell me which one is right (LIPET or LIATE)? Also, in trig, which one come first? sin,cos or tan? thxHomework Equations The Attempt at a Solution
  49. C

    Integration using separation of parts

    Homework Statement evaluate the integral cos^-1 2x dx? Homework Equations The Attempt at a Solution let u = arc cos du = -1 / (sqrt 1-x^2) dv = 2x v= x^2 arc cos * x^2 - the integral of -x^2 / (sqrt 1-x^2) then i don't know what to do
  50. L

    Black Hole Diagram: Parts, Types & More

    Im trying to come up with a sort of diagram you could call it, of a black hole and all its "parts" for example i know there's the event horizon, ergosphere, the jets that come out of the poles. And any other helpful info. about black holes and there classification, like there's rotating ones...
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