Read about integration by parts | 19 Discussions | Page 1

  1. B

    Integrating a fraction with three variables: ( sin(a) + M^2 ) / ( 1 + x^2 )

    I think in the case of "n da" you can see the denominator (1+x^2) as a constant, so ∫ ( sin(a) + M^2 ) / ( 1 + x^2 ) da = ( 1 / ( 1 + x^2 ) ) * ∫ (sin(a) + M^2 ) da = ( 1 / ( 1 + x^2 ) ) * ( -cos(a) + (M^2)a ) = ( - cos(a) + (M^2)a ) / ( 1 + x^2 ) --- Is this the way to go? This is my...
  2. acalcstudent

    I Bernoulli Equation with weird integral

    Part of me thinks this is could be a u-sub b/c x^3's derivative is 3x^2, a factor of 3 off from what e is raised to...but it is not a traditional u-sub...any thoughts if this is a u-sub or by parts, and what u should be? I know that there is more to solving the equation after this ( z =...
  3. physics bob

    I Integral equation

    The book on quantum mechanics that I was reading says: d<x>/dt = d/dt ∫∞-∞ |ψ(x,t)|2 dx =iħ/2m ∫∞-∞ x∂/∂x [ψ∂ψ*/∂x+ψ*∂ψ/∂x]dx (1) =-∫∞-∞ [ψ∂ψ*/∂x+ψ*∂ψ/∂x]dx (2) I want to know how to get from (1) to (2) The book says you use integration by part: ∫abfdg/dx dx = [fg]ab - ∫abdf/df dg dx I chose f...
  4. R

    I Integration by parts

    Hi, I've been following a derivation of relativistic kinetic energy. I've seen other ways to get the end result but I'm interested in finding out where I've gone wrong here: I'm struggling with integrating by parts. The author goes from...
  5. P

    I Integrating sqrt(x) cos(sqrt(x)) dx

    Question: sqrt(x) cos(sqrt(x)) dx My try: Let dv = cos(√x) => v = 2√xsin(√x) and u = √x => du = dx/(2√x) Using integration by parts, we get ∫√x cos(√x) dx = 2√x√x sin(√x) - ∫(2√xsin(√x) dx)/(2√x) = 2x sin(√x) - ∫sin(√x) dx = 2x sin(√x) + 2 cos(√x) √x However, the answer given in the book...
  6. Prof. 27

    Difficult Integral

    Homework Statement Hi, I'm doing a variation of parameters problem for my differential equations class. It requires solving the integral: ∫ex t-2 dt I am sure my professor did not give me an impossible integral and that there is some algebraic "trick" to solving it, but despite going through...
  7. Elvis 123456789

    Integration by parts and approximation by power series

    Homework Statement An object of mass m is initially at rest and is subject to a time-dependent force given by F = kte^(-λt), where k and λ are constants. a) Find v(t) and x(t). b) Show for small t that v = 1/2 *k/m t^2 and x = 1/6 *k/m t^3. c) Find the object’s terminal velocity. Homework...
  8. E

    A Triple Product in Laplace Transform

    Hello - I'm not sure this is where this should go, but I'm working with Laplace Transforms and differential equations, so this seems as good a place as any. Also, I doubt this is graduate level math strictly speaking, but I went about as high as you can go in calculus and linear algebra during...
  9. Electgineer99

    Integration by parts

    |3^xlog3dx I don't even know where to start. I know that the formula is |u.dv = uv - |v.du u=3^x v=log3
  10. C

    Integration by parts

    Homework Statement [/B] Homework Equations ∫ f(x) g'(x) dx = f(x) g(x) - ∫ f '(x) g(x) dx f(x)=√(1+x^2) f '(x)=x * 1/√(1+x^2) g'(x)=1 g(x)=x The Attempt at a Solution ∫ √(1+x^2) * 1 dx =x * √(1+x^2) - ∫ x^2 * 1/√(1+x^2) dx Further integration just makes the result look further from what...
  11. F

    Stuck in Integrating e^(i*x)cos(x)

    I'am trying to prove \int e^{ix}cos(x) dx= \frac{1}{2}x-\frac{1}{4}ie^{2ix} Wolfram tells so^%28i*x%29cos%28x%29&random=false But I am stuck in obtaining the first term: My step typically involved integration by parts: let u=e^{ix}cos(x) and...
  12. F

    Unusual Limit involving e

    This was just very basic, I have accepted it in just a heartbeat, but when I tried to chopped it and examined one by one, somethings fishy is happening, this just involved \int_{0}^{\infty}x e^{-x}dx=1. Well, when we do Integration by parts we will have let u = x du = dx dv = e^{-x}dx v =...
  13. RaulTheUCSCSlug

    Average Speed for Maxwell's Distribution of Molecular Speed

    Using the Maxwell-Boltzmann equation above, there is an example in my book (Giancoli 4th edition p. 481) where they use this to find the average velocity. I understand that it would just be the sum of all the speeds of the molecules divided by the number of molecules. But then I'm having...
  14. Abtinnn

    A problem with Integration by Parts in Hartle's "Gravity"

    Hi guys! I am reading the book "Gravity" by Hartle. I came across this scary-looking integral. The author does integration by parts and I don't get how he does it. Could someone guide me please? Relevant equations: ∫u dv = uv - ∫v du
  15. F

    Help with an intermediate integral

    Homework Statement I have been trying to evaluate an integral that has come up in the process of me solving a different problem, but am completely stuck. As I have confirmed with Wolfram Alpha that the integral once solved yields the correct solution to my problem. However, I am trying to...
  16. M

    Integrals and gamma functions manipulation

    Homework Statement I am working through some maths to deepen my understanding of a topic we have learnt about. However I am not sure what the author has done and I have copied below the chunk I am stuck on. I would be extremely grateful if someone could just briefly explain what is going on...
  17. E

    A (relatively) simple QM Problem, but seeking my mistake

    Homework Statement Find <r> and <r2> for an electron in the ground state of hydrogen. Express in terms of Bohr radius. Homework Equations We know the relevant wave functions are: R_{10} = \frac{c_0}{a}e^{r/a}Y^0_0 and Y^0_0 = \frac{1}{\sqrt{4\pi}} The Attempt at a Solution As I...
  18. Mr. Rho

    Question about mathematical equality

    Hi there, im reading Chapter 9 of Jackson Classic Electrodynamics 3rd edition, and I don't see why this equality is true, it says "integrating by parts", but I still don't know... any help? [Broken]
  19. kelvin490

    Question about substitution method in integration

    It is common that we replace \int u(x)v'(x)dx by \int udv where both u and v are continuous functions of x. My question is, must we ensure that u can be written as a function of v before applying this? The above substitution method is involved in the proof of integration by parts but I cannot...