Integrating Definition and 940 Threads

Homework Statement (2sinx - 5e^x) The Attempt at a Solution is it just... -2cosx - 5e^x

What does it really mean to integrate over all possible fields in the Path integral formulation of quantum field theory,and how does such a formalism goes out to decribe field quanta? Another question is im new to Quantum field theory i was wondering whether i should stick to the old...

Quick integrating question...(part of a series question) Still studying for my exam... Came across this example and I don't know what the method is for integrating this type of problem? (I'm using it to do the integral test for series). How did they get rid of the x^3? thanks for the help :-)

Hello! I need to calculate \int_{-\infty}^{\infty} x^{2} e^{-\frac{|x|}{b} dx and I know the answer should involve \pi. I've tried splitting the integral for x and -x with limits from 0 to infty and -infinty to 0, which gives me the answer of 2b. But I don't think this is correct. Does...

Homework Statement I'm actually in the middle of a multivariable question, and I am stuck because I don't remember how to integrate sin(\phi)cos(\phi) . The Attempt at a Solution I have an understanding of the material, but I can't remember how to integrate this. Someone please refresh...

Okay so I am suposed to evaluate 2 of these: 1.) \int\sin^3(a\theta)d\theta the solution manual looks like it used a trig ID to do this. Why?? Doesn't \int\sin^3u du=\frac{1}{3}\cos^3u-(\cos u)+C ? So just use the u-sub u=a\theta \Rightarrow du/a=d\theta So it should just be...

Homework Statement \int {\frac{{dx}}{{\sqrt {x^2 - 2} \left( {x^2 - 1} \right)}}} Homework Equations \frac{d}{{dx}}\arctan (x)The Attempt at a Solution \frac{d}{{dx}}\arctan (x) seems to be part of it, I can't quite get much farther...

Hi, I'm learning differential equations, and although I understand the methods I have learned thus far, I often have trouble seeing what is the reasoning behind them. Take for example, the use of the integrating factor when solving first order linear ODE's. I understand how to use it, but...

Homework Statement \int \frac{dx}{(x+1)(x^2+1)(x^3+1)} The Attempt at a Solution I tried to solve it in 3 ways. 1)\frac{A}{(x+1)}+\frac{B}{(x^2+1)}+\frac{C}{(x^3+1)} 2)\frac{A}{(x+1)}+\frac{B+Dx}{(x^2+1)}+\frac{C+Ex}{(x^3+1)}...

Let a0, a1, a2, a3 be arbitrary real numbers, and let f(x) = a0 + a1*x + a2*x^2 + a3*x^3 Show that the approximating the integral \int f(x)dx[/tex] ( Couldn't figure out the bounds using latex but the integral is from pi to 42) with Simpson's rule yields the exact value of this integral...

[SOLVED] Integrating with Change of variables -method Homework Statement Solve by "Change of variables"-method ∫(dx)/(eˆx + eˆ(-x)) Homework Equations ∫f(x)dx=∫f(x(t))*x'(t)dt The Attempt at a Solution ∫(dx)/(eˆx + eˆ(-x))=∫(eˆx)/(1 + eˆ2x) t=eˆx x=ln...

Homework Statement \int4x^-3*ln(9x) Homework Equations \int u'*v = u*v - \int u*v' The Attempt at a Solution i know the answer is \frac{-2ln(9x)-1}{x^2} but i don't understand the step \int u*v' if any could help me...thanks

As usual I did this question I'm working on backwards, doing the section dealing with air friction first. Now realizing I must do the 'first part' and I think I am over thinking again. With no air resistance, I need the position of a trajectory from Newton's second law. I know gravity is the...

1. Solve the equation [sin(xy) + xycos(xy)]dx + [1 +x^{2}cos(xy)dy = 0 Homework Equations The Attempt at a Solution [sin(xy) + xycos(xy)]dx = M(x,y) [1 +x^{2}cos(xy)dy = N(x,y) dM/dy sin(xy) = xcos(xy) xycos(xy) = uv' + vu' = (xy)(-xsin(xy)) + (x)(cos(xy)) u = xy du = x...

[SOLVED] More help in integrating Homework Statement Find a,b,n such that a,b are rational and n is not an element of Z. a>0,b<0 \int_{0}^{1} \frac{3x}{\sqrt{1+6x-3x^2}} = \frac{\pi}{a^n} + b Homework Equations \int \frac{1}{\sqrt{A^2-X^2}} dx= \arcsin{\frac{X}{A}+K \int \frac{x}{R} =...

I need to find the integral of (1/(1+e^x)) dx. ...I don't think I can use u substitution, but well, I'm basically open to suggestions.

I have a set of measurements that form a plot in MATLAB. I just want MATLAB to integrate (ie. find the area) in a certain region of x values...is this possible? All the integration functions I've seen require a function file or some sort of function...

My own question, carried to a new thread as not to derail another:

i'm at a loss about how to do this type of integration. can some one show me how to evaluate the integral of (d^3)k exp[ik*(x1-x2)]/[(k^2+m^2)(2pi)^3], where "*" is the dot product between the 3 vector k and (x1-x2), which are both 3 vectors. this come from the energy equation used to get the...

Homework Statement Use the integrating factor to solve the first order differential equation dy/dx + (2/x)y = 1 - 2/x subject to the initial condition y(1) = 2The Attempt at a Solution I have the full answer (it's an example), but my lecturer is notorious for omitting steps, to my constant...

Homework Statement \int_0 ^\pi \sqrt{1-\sin^2 x} dx Homework Equations 1 - \sin^2 x = \cos^2 x The Attempt at a Solution I don't know how to treat this since cos changes sign half way across the integral. I know the answer should be 2 but I keep getting 0 every which way I try.

I'm having real problems integrating a natural log. The problem I have been set is (where S = integration sign) S (x - 2) Ln(3x) I'm trying to use the integration by parts rule but keep getting the wrong answer and I think it might be to do with the natural log. I have used f(x) =...

\int x^xdx After calculus today, our professor casually asked us to integrate the above problem. Most of us stated DNE (does not exist), or possibly x+1 / x+1 . He stated that both of these solutions were incorrect and than challenged us to write a paper on the subject which seemed...

Hello everyone I'm stuck with a problem from Simmons (not HW). The problem asks to solve the following equation by finding an integrating factor (xy-1)dx + (x^2 - xy)dy = 0 I found by hit and trial that there can be no integrating factor that is a function of x alone or y alone. So how...

Homework Statement no specific problemsHomework Equations x center of mass = moment about y/total area y center of mass = moment about x/total area The Attempt at a Solution ok, so I am in AP calculus, and since the AP testing has ended, we've done some random topics, such as centroids of...

Hey, I am in high school AP Physics/Calculus and my group needs to come up with a project that involves both the use Physics and Calculus. We are willing to research and do anything. Does anyone have any interesting topics that they could share with us. By the way, we CANNOT do a project on...

Need help, soon please! Integrating I am struggling to integrate this function since last night but,it seems like it is a dead end doing it. how would you integrate this function integral x^n e^(-x^(n-1)) dx i tried the parcial method, and went like this integ x^(n-2) x^2...

Homework Statement Final round I promise! Is there some sort of trick that can be applied to the following equation so that it is easier to process? \frac{dy}{dt}=\frac{1}{t+y},\:y(-1)=0 The Attempt at a Solution Somebody told me that the equation can be made easier by...

Homework Statement y' (1+e^t) + e^ty = 0 How do I get it in the form y' +f(t)y = f(p) That is how do apply algebra to this so it is in the proper form to process it? The Attempt at a Solution Kind of hard to post my attempt. I can move the y' (1+e^2) to the right side then divide both...

Homework Statement y' + 2ty = t^3 Homework Equations Integrating factors and variation of parameters The Attempt at a Solution Ive solved for m M = e^{\int 2t\,dx} M = e^t^2 (this is e^t^2, but doesn't look like it in latex) I multiplied both sides by M (e^t^2)(y') + (e^t^2)(2ty) =...

Is there a way other than trial and error to tell whether an integrating factor h is a function of x only, y only, or of x and y?

I want to integrate (cos(x))^4, but I can't find a formula for (cos(x))^n in my collection. What is the way to integrate this?

From an example in my book: Int Int (2x) dxdy over R = 0 (R is the circe x^2+(y-1)^2=1) How can one make this conclusion without integrating?

Hi. I've been struggling with this for hours and not getting anywhere even after a hint from a teacher. I have to integrate (indefinite integral) v / (1+cv²) where c is a constant. The hint the teacher gave was that the integral of 1 / (1+v²) is tan^-1(v), but I can't see how to use this...

How would you integrate this equation?

Ok well The integral is : \int \frac{1}{\sqrt{1-x^2}} \frac{1}{\arcsin x} dx. I can tell by inspection, it being of the form f'(x)/f(x), that the answers ln (arcsin x), but I was hopping Integration by parts could do it for me as well. But here's my Problem: u=1/(arcsin x) du=(-1)/...

Homework Statement How do you integrate a product of two trigonometric functions of x, when the argument is different, ie: what is the integral of sin x cos 3x I ought to know this, but don't seem to be able to do it. Thanks in adv! Homework Equations The Attempt...

I don’t know how to integrate the Maxwell-Boltzmann distribution without approximation or help from Maple. Given the Maxwell-Boltzmann distribution: f(v) = 4*pi*[m/(2*pi*k*T)]^(3/2)*v^2*exp[(-m*v^2)/(2*k*T)] Assuming a fixed temperature and mass, one can simplify this equation: f(v)...

I have to integrate over the northern hemisphere of a sphere. The answer states that the integration bounds for r is 0 to R, for theta it's 0 to pi/2, for phi it's 0 to 2pi. What I don't understand is why theta doesn't go from 0 to 2pi. If I had to set this up, I would have theta going from 0...

Homework Statement I'm being dead thick, but I can't remember how to integrate an exponential function. \int x^3e^{-\alpha x^2}dxHomework Equations The Attempt at a Solution I reckon that this shouldn't be too complex, but I've totally forgotten how to go about this question. The x^3 term means...

Homework Statement To find the voltage-current relationship of a capcitor, integrate both sides of i = C(dv/dt) The Attempt at a Solution In the book they say, v = (1/C)(The Integral from -tve infitity to t) of i dt. or v = (1/C)(The Integral from tnot to t) of i dt + v(tnot)...

I know that \int \tan^{2}x dx= \int \sec^{2}x-1\ dx = \tan x - x + C but i don't completely understand how this is derived. Because of this lack of comprehension, I have no idea what to do with \int \sec^{4}5x\ dx. I went from there to get: \int \sec^{4}5x\ dx= \int [\sec^{2}5x]^{2}\ dx= \int...

I Just want to know if this is how this should be done.. \frac{dy}{dx} = \frac{3y^2}{x} dy = \frac{3y^2}{x}dx dy = 3^2 x^-^1dx \frac {1}{3} \int \frac {dy}{y^2} = \int x^-^1dx \frac {1}{3} ln| y^2| = ln | x | + C because I forget how to integrate the polynomial...

Homework Statement Find the integral of: Homework Equations x^2 . sinx dx (With upper and lower limits of pi and 0 respectively.) The Attempt at a Solution Integrating for the first time: -x^2 . cos x + 2 [integral of] x . cosx dx After integrating a part of my first...

Homework Statement solve the following equation using method of intergrating factors: Homework Equations dy/dx = y + cosx - sinx The Attempt at a Solution i think i have to get it in the form dy/dx + r(x)y = f(x) but i can't see how, if i multiply or divide by a factor i...

Find the two integrals: \int_0^{\infty}\frac{e^{-\alpha x^2}}{x^2+1}\sin(\alpha x) \, dx \int_0^{\infty}e^{-\beta^2t}\cos(\beta x) \, d\beta Any hint?

Suppose you have an equation: M(x,y) dx + N(x,y) dy = 0 I have heard that there always exists an integrating factor u(x,y) such that the partial derivative of uM with respect to y equals the partial derivative of uN with respect to x. But somewhere in the back of my mind I remember that...

Hi, i have a problem which is confusing me :confused: Question: Given that \int_{0}^{\infty}e^{-ax^2} dx = \frac{\sqrt{\pi}}{2\sqrt{a}} What is (i) \int_{0}^{\infty}e^{-ax^2} x^2 dx (ii) \int_{0}^{\infty}e^{-ax^2} x^3 dx (iii) \int_{0}^{\infty}e^{-ax^2} x^4 dx It tells me...

I am trying to integrate the the normal vector to the surface of a hemisphere but am having some trouble. I am pretty sure that the x and y components will cancel out, and that the z component in spherical coordinates is R*Cos[theta] but for some reason I am having trouble really understanding...

The task is to find one primitive function to: (4x-3)^2 This was quite straightforward. Or so I though. It can easily be turned into 16x^2 - 24x + 9 and then integrated to \frac {16x^3}{3} - 12x^2 + 9x choosing C = 0 Then I started to think. Couldn't this be integrated...