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. I

    What are the steps for using Integration by Parts to evaluate an integral?

    Homework Statement #1. Use Integration by parts to evaluate the integral \int 2x \ln(2x) dx #2. Use Integration by parts to evaluate the integral \int (\ln(3x))^{2} dx #3. Use Integration by parts to evaluate the integral \int x e^{4x} dx #4. Evaluate the indefinite integral. \int \sin(3x)...
  2. N

    Help With Parts III & IV - Stuck on Double Angle Formula

    http://img103.imageshack.us/img103/637/trigrb3.th.jpg I was having trouble with parts iii and iv. I have done i and ii. Please can someone help me with iii and iv. I do not really know where to start for iii and hence iv. I was thinking about the double angle formula for tan, but didnt...
  3. S

    Nuclear Reactor With No Moving Parts

    There's an article in the May 12 2008 New Yorker Magazine by Malcolm Gladwell, in which he talks about brainstorming sessions by teams of inventors headed by Nathan Myhrvold. One of the ideas is a small Nuclear Reactor with no moving parts. Supposedly the core would be about 3x10 meters...
  4. Z

    What is the error in my integration by parts?

    Hi, I am trying to integrate (x^5)/7680 . exp (-x/2) dx between 0 and 1. I've had various attempts at this and this is what i have done so far... Taken the 1/7680 outside the integration Using integation by parts I have assigned u=x^5 and dv/dx = exp(-x/2). when i integrate exp(-x/2) i...
  5. F

    Integrate that by parts for integral

    i need help taking this integral \int 9sin\sqrt{t+1} help please! i don't even know where to start :[
  6. C

    Integration by parts tanx help

    I actually have two here, so I will just list both: Homework Statement \int\frac{x}{x^{2}+4x+4}dx Homework Equations None The Attempt at a Solution I tried this one twice. I honestly have no idea how to do it, and I used integration by parts. The first time, I reduced it down...
  7. H

    Integration by Parts: Solving y = arcsinh(x)

    Homework Statement Use integration by parts to find: y=... if dy=arcsinh(x) dx Homework Equations int(v.du)=uv-int(u.dv) The Attempt at a Solution I understand how to perform integration by parts. My problem here is, what are my 'v' and 'du'?
  8. C

    Antiderivative of arctan and x function (by parts maybe? )

    antiderivative of arctan and x function (by parts... maybe??!) find antiderivative of 2xarctan(8x) { = antiderivative s thing. I did it by parts at first and got x^2arctan(8x) - 8 * { (x^2)/(1+64x^2) To get the antiderivative of the second part i did it by parts again and that...
  9. S

    Complex Integration by Parts Help. Please

    Hi Can anyone help me with this integration. I will use I to symbol the integer sign Limits between 1 and 0 Ie^-x.Sinxdx I understand I have to integrate by parts and get the following answer, ignoring the limits for the time being. Ie^-x.Sinx = e^-x.Cosx I -Cosx.e^-x dx then i...
  10. N

    Integration by parts expression

    Use integration by parts to express: I (n) = ∫(sin)^n (x) dx in terms of I (n-2) Let u = sinn-1 x du = (n-1)sinn-2 x cos x dx v = - cos x dv = sinx dx so integration by parts give: ∫〖sin〗^n x dx= -cos⁡〖x 〖sin〗^(n-1) x+(n-1) ∫〖sin〗^(n-2) 〗 x cos^2⁡〖x dx〗 Since cos2x = 1 –...
  11. S

    What is the Integration by Parts Method for Solving Complex Integrals?

    I need to integrate 2\int_0^1cosh(\pi x)cosnx Not asking anyone to do it for me, just what method to use? Thanks alot.
  12. A

    Rayleigh Flow - Integration By Parts

    Hello, This is not a question regarding a homework problem, but a step in class the professor did not show how to calculate. Homework Statement I am taking a course on Viscous Flow, and for Rayleigh flow after applying the similiarity solution : \eta=(y/(2*\sqrt{\gamma*t})) The...
  13. L

    Integrate by Parts: Solve \int e^{x}sinxdx

    [SOLVED] Integration by parts 1. Evaluate \int e^{x}sinxdx [Hint: Integrate by parts twice.] I can't seem to get an answer, but by integrating, the process is redundant (repeats itself). Thanks Work: \int e^{x}sinxdx Let u = sin x, therefore du = cosxdx Let dv = e^{x}dx...
  14. S

    Difficult integral by sub., parts & table

    Homework Statement \int xe^{2x^2} cos(3x^2) dx This is the hardest integral I've attempted so far. I've come up with an answer that fits a table in my book but I'm not sure if I arrived there correctly. Thanks for reading! Homework Equations \int e^{au} cos\ bu\ du\ =...
  15. M

    Real & Imaginary Parts of Logarithms

    Homework Statement Find the real & imaginary parts of log(1+i)log(i) ? Homework Equations The Attempt at a Solution
  16. B

    I need SERIOUS HELP integration by parts

    I need SERIOUS HELP...integration by parts! Homework Statement Integrate: x^3*e^x Homework Equations The Attempt at a Solution I have the answer in my book but I am not understanding why you have to repeat the integration 3 times... 1.) dv = e^x dx v = e^x u = x^3 du =...
  17. G

    MathCAD - separation of real and imaginary parts of a complex variable

    Hi guys, just wondering whether you could help. I've got a complex number in terms of a lot of variables, and need to separate it into its real and imaginary parts. How do I do that? I spent past hour trying to look for tutorials, unfortunately none tells you how to do it...
  18. G

    Integration by Parts Homework Help - Q2

    Homework Statement In preparation for an exam next week, I'm solving some of the end-of-chapter questions. There are 30 questions. I've solved a few on my own, but here's one I'm getting stuck on. Question 2) \int x5^x dx, problem here is I don't know how to deal with 5^x. The correct...
  19. P

    Integration by parts (multivariable)

    Homework Statement I can find on Wikipedia the "formula" for integration by parts for the case where there is a multi-variable integrand, but I would like to know what substitutions to make in order to show my steps. Homework Equations For multiple variables we have...
  20. I

    So, please show your work, and explain where u have any difficulty.

    Integration by Parts HELP! Hey, I am working on some calculus and I am having some trouble with the last few integration by parts problems. I got the first couple, and i grasp the concept of integration by parts but for some reason I just can't figure these 3. Any help would be greatly...
  21. I

    Need Help with Integration by Parts? Check Out These Tricky Problems!

    Integration by parts HELP! Hey, I am working on some calculus and I am having some trouble with the last few integration by parts problems. I got the first couple, and i grasp the concept of integration by parts but for some reason I just can't figure these 3. Any help would be greatly...
  22. J

    Integration by parts and roots

    Ok. I have a definite integral of e^sqroot(x) dx from x=0 to x=1. I would use u=sqroot(x) and du=1/2*sqroot(x), but I'm confused what I would set v=?
  23. GarageTinker

    Good Source/s for Mechanical Parts?

    Does anyone know of any good sources for mechanical parts that already on the market? In my "Garage Tinkering" hobby, as much as possible, I like to use parts and materials that are already available on the market instead of having to manufacture them.
  24. M

    How to Correctly Apply Integration by Parts to ln(x-7)?

    [SOLVED] integration by parts question Homework Statement This is part of a larger problem but I'm just not sure if I have the right answer. edit: this is integral of ln(x-7)dx i just can't seem to figure out how to make it in latex Homework Equations The Attempt at a Solution...
  25. G

    Possible Integration by Parts Exam Practice Problems

    Homework Statement Got an exam later today on this, just looking for some practice. I know this is kinda reverse of what the forum is intended for, but I'd like to ask for people to post some problems that I can solve via Integration by Parts. Just like 5 or so. Homework Equations...
  26. M

    SOLVED Integration by Parts Question

    [SOLVED] integration by parts question Homework Statement I think my first problem is at integration by parts, but let me know if you see a different error in my work. Edit: I shoud mention that this is Calculus 2 and we just learned first order differential equations today. So I don't...
  27. S

    Reduction Formula and Integration by Parts

    I was sick and missed class:rolleyes: ∫ sin^2x dx = x/2 – sin2x/4 + C (I see that there is a trig identity in the answer as sin2x = 2sinxcosx) What I tried (copying the example in the book) u = sinx du = sinxcosx dx (why is du not cosx?) v = -cos x dv = sinx dx (why is this...
  28. B

    Integration problems. (Integration by parts)

    Homework Statement Hi, I have a test coming up soon so I was doing some questions from the textbook when I stumbled upon this one and I'm stuck after like 5 tries. Here is the question: \intcos^2(x)dx Solve. Homework Equations the question then states we should solve using this...
  29. R

    Intergration by Parts (IbP) problem

    \int_{1} ^{2e} x^2(ln x)^{2} dx I need to solve this using IbP. I made the following: u = (ln x)^2 du = (\frac{2 ln x}{x}) dx dv = x^2 dx v = \frac{x^3}{3} So I get: (ln x)^2 (\frac{x^3}{3}) \|_{1} ^{2e}- \int_{1} ^{2e} (\frac{x^3}{3}) 2 ln x dx (not sure how to make...
  30. T

    How can I find the intersection of two vector spaces with given basis vectors?

    i have solved a full question (except the last part which i tried to come up with some formula but that didnt work out) i showed every step of the way unfortunetly i don't have the answers to this question so can you tell me if i solved wrong some subquestion and how to solve the 5th it a...
  31. E

    Integration by Parts, 1/x dillema

    the answer to \int\frac{1}{x}(dx) is lnx +c. but if you do it with integration by parts, you end up with \int\frac{1}{x}(dx) = 1 + \int\frac{1}{x}(dx) which comes to 0=1. why does this happen?
  32. P

    Maze generation algorithm for specified parts

    I am an undergraduate student studying mechanical engineering. We are doing a project called the labyrinth cutter, we're constructing a piece of artwork consisting of a a gantry connected to a cutter head. The cutter is supposed to cut out a labyrinth to a piece of music. I decided to use the...
  33. M

    Will Speedy Sue Collide with the Van in the Tunnel?

    Homework Statement Speedy Sue, driving at 35.0 m/s, enters a one-lane tunnel. She then observes a slow-moving van 155 m ahead traveling at 5.30 m/s. Sue applies her brakes but can accelerate only at -2.00 m/s2 because the road is wet. Will there be a collision? yes If yes, determine...
  34. F

    How to Solve for A, B, and C in x^2+4x-2=A(x+2)(x-2)+Bx(x-2)+Cx(x+2)

    Homework Statement x^2+4x-2=A(x+2)(x-2)+Bx(x-2)+Cx(x+2) How to find A, B and C? Homework Equations Answer is A=1/2, B=-3/4, C=5/4. The Attempt at a Solution A+B+C=1 A(2-2)+B(0-2)+C(0+2)=4 A*2*(-2)+B*0*(-2)+C*0*2=-2 A+B+C=1 0A-2B+2C=4 -4A+0B+0C=-2 C=2+B A=1/2...
  35. L

    Integration by Parts: Solve 8x^{3}\ln\!\left(x\right)

    The teacher kinda skipped over this and expects us to know how to do it. Being I can't understand what he is saying, I'm kinda lost, so I missed how to do the whole u, du thing. Homework Statement Solve \int{ 8x^{3}\ln\!\left(x\right) \, dx} using Integration by Parts. Homework...
  36. M

    SOme help with intergration by parts,

    SOme help with intergration by parts, please [b]1. Find: \int e^x cos (x) dx The Attempt at a Solution I tried using integration by parts - what we are working on... all these 3 possibilities: u = cos x, u= e^x, u = e^x cos(x) And the \int vdu are, respectively: 1. \int e^x sin(x) dx...
  37. I

    Soving an eqn with exponential & linear parts

    Homework Statement Known Constants A, B and C Unknown (we are solving for) t e is the exponential as in ln(e) = 1 Homework Equations e^{t*A} + t*B + C = 0 (we want to solve for t) The Attempt at a Solution This is not for school or anything. This is actually part of an...
  38. B

    Integration by Parts: Help Needed with x^2 e^x^3 dx

    Homework Statement Integrate x^2 e^x^3 dx Homework Equations I = uv - integral of u'v The Attempt at a Solution I don't know where to begin this question at all and have been stuck on it for the past half hour. Any help would be really appreciated. :(
  39. M

    Solve Integration by Parts: Help with First Steps

    Homework Statement I have tried this question a number of times, but to no avail. Could somebody please help with the first couple of lines, thank you. \int_0^x2cte^{-ct^2}dt where c is a postive constant Homework Equations The Attempt at a Solution Let u=t and let dv=2ce^{-ct^2}dt
  40. S

    Integration By Parts: Solving \int e^{2x}sin(e^x)dx

    Homework Statement \int e^{2x}sin(e^x)dx Homework Equations Can I make the substitution: w = e^x ; dw = e^x dx Making a "new / simpler" problem: \int w sin(w) The Attempt at a Solution Using integration by parts on the "new" problem: u = w ; dw = du dv =...
  41. quasar987

    Integration by Parts: Solving for the Error in a Tricky Integral

    [SOLVED] Integration by parts Homework Statement I've been staring at this for 30 minutes and can't figure out what's wrong. I end up with 1/xi instead of xi. The book says, \int_{-\infty}^{+\infty}te^{-t^2/2}\sin(\xi t)dt=\int_{-\infty}^{+\infty}e^{-t^2/2}\xi \cos(\xi t)dt The...
  42. R

    Learn How to Integrate xlnx Using the Integration by Parts Method

    little help? simple question... Homework Statement Integrate: xlnx dx use integration by parts Homework Equations The Attempt at a Solution let u = x du = dx dv = ln x v = ??
  43. A

    Integration by Parts: Solving ∫sin²x dx with Ease

    how would one integrate by parts the following: \int sin^2xdx thanks!
  44. A

    Can integration by parts (and other int related Q's)

    Be used to prove that a constant coefficiant can be taken out the integral? such as 2x just being 2 multiplied by the integral of x? \int{2x} = 2\int{x} Also, what is the integral of 0? Is it 0 or "c"? I'm mainly asking because I recently got dropped with a Fourier series homework and its...
  45. E

    Linear Systems Question (Several Parts)

    Homework Statement Find the complete response of the system represented by y''(t)+2y'(t)+y(t)=u(t), y(0^-)=1, y'(0^-)=2 and identify the zro-state and zero-input response components. Find the system transfer function and the system impulse response. Homework Equations...
  46. N

    Integration by Parts in Zee's QFT: Understanding Eq. (14) to Eq. (15)

    Homework Statement I'm studying from Zee's QFT in a nutshell. On page 21, I don't understand how he uses integration by parts to get from Eq (14) to Eq (15), ie from Z = \int D \varphi e^{i \int d^4 x \{ \frac{1}{2}[(\partial \varphi)^2 - m^2 \varphi^2] + J\varphi \}} to Z = \int D \varphi...
  47. Saladsamurai

    Integration by parts VS. Formula in text

    I am either making the same mistake repeatedly, or I can't factor! I did this \int\ln(2x-3)dx first by parts and then using the formula \int\ln u du=u\ln u-u+C By parts I got: u=\ln(2x-3) dv=dx so =x\ln(2x-3)-\int\frac{2x}{2x-3}dx and by long division: =x\ln(2x-3)\int...
  48. Saladsamurai

    Stupid Tabular Method for Integration by parts

    Is this the correct way to use the Tabular Method for \int x^2e^{-5x}dx repeated diff: x^2 2x 2 repeated Integration: e^{-5x} -\frac{1}{5}e^{-5x} \frac{1}{25}e^{-5x}...
  49. D

    How do I solve \intarctan(1/x)dx?

    [SOLVED] Integration by parts help. Homework Statement I'm working on ym Math assignment, and we are currently doing Integration by parts. I haven't had too much trouble except with the last 3. Ill only post the first of those 3 for now. I need to find \intarctan(1/x)dx Homework...
  50. K

    Need help with difficult integration by parts problem

    Homework Statement integrate: (x^3) e^(3x^2) dx Homework Equations uv- integral vdu The Attempt at a Solution i've tried this many times on paper and can't get the right answer. I'm starting to get really frustrated. Please help...
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