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...
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 =...
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...
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...
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...
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...
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...
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...
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...
I'am trying to prove
\int e^{ix}cos(x) dx= \frac{1}{2}x-\frac{1}{4}ie^{2ix}
Wolfram tells so http://integrals.wolfram.com/index.jsp?expr=e^%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...
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 =...
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...
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
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...
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...
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...
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?
http://imageshack.com/a/img673/9201/4WYcXs.png [Broken]
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...