What is Integrate: Definition and 650 Discussions

Homework Statement given: A wire loop with a circumference of L has a bead that moves freely around it. The momentum state function for the bead is ## \psi(x) = \sqrt{\frac{2}{L}} \sin \left (\frac{4\pi}{L}x \right ) ## find: The probability of finding the bead between ## \textstyle...

How is this done? My textbook only specifies integrating polar graphs with respect to theta.

Homework Statement Integrate: cos2x/[cos^2 (x).sin^2 (x)] Homework Equations [/B] ▪cos2x=1-2sin^2 (x) ▪2sinxcosx=sin2x ▪1/sinx = cosecx ▪Integration of cosec^2 (ax+b)=[-cot(ax+b)]/a ▪Integration of sec^2 (x)=tanx The Attempt at a Solution I have attached my solution,but the answer is not...

I'm trying to integrate a simple function (x*y) using the Romberg method. Question 1: I want to integrate only x and maintain the argument y present in the rest of calculation, like a global variable. In fortran 77 I would use common. Question 2: How to integrate using arguments in the...

Homework Statement Integrate sin (x^0.5) Homework EquationsThe Attempt at a Solution I let u = sin (x^0.5) , du/dx = cos [(x)^0.5 ] ( 1/ (x)^0.5 ) , how to proceed ? [/B]

Homework Statement I need to find the coefficients for a Fourier expansion. Here is the integral I need to solve: (1/π) ∫sin(x/2)sin(nx)dx where the limits are from -π to π. The original function for the expansion is f(x) = sin(x/2) Homework Equations None The Attempt at a Solution Should I...

Hello there, I've been considering the geodesic equations of motion for a test particle in Schwarzschild geometry for some time now. Similar to what we can do with the Kepler problem I would like to be able to numerically integrate the equations of motion. I'm quite interested to see how...

Homework Statement Suppose you have a Triangle with the vertices, (0,0) (1,1) and (0,1). Integrating along that path. I have some differential function dZ where Z = Z(x,y) Homework EquationsThe Attempt at a Solution [/B] If I need to integrate, then I need to find the limits of...

Homework Statement How do I go about integrating ##(\frac{1-x}{1+x})^{\frac{1}{2}} ##? Homework Equations above The Attempt at a Solution im not really sure. could integrate by partial fractions if it was to the power of ##1##, only thing i can think of thanks in advance

Homework Statement Hello people How would one integrate a function in the form of ∫ ydx/(x2 + y2)3/2 Homework Equations I don't really know how to go about it The Attempt at a Solution I tried solving it by substitution but I can't find a suitable one... any online tutorials for such an...

Homework Statement Hi, Please see attached. I am trying to show the second equality , expressing all as a total derivative (I can then show that ##\delta S = ##) Homework Equations See above The Attempt at a Solution So the ## m ## term is pretty obvious, simply using the chain rule. It...

Sorry i have one question to ask how to integrate the electric field of the square sheet( see the pink circle below) it looks hard for me thank you very much

Homework Statement I know that in general it is when the gravitational field is not constant, so that part is fine. To find the gravitational force between a sphere with mass M and a radius R and a thin rod of length L and mass m which has one end a distance x away from the center of the...

Homework Statement I'm trying to integrate this equation so that I can find my position using my initial drag force and initial velocity. V/(-g-kv) dv Homework Equations The Attempt at a Solution U substitution won't work Integration by parts won't work Partial fractions won't work. It...

Sorry how to integrate this function from step1 to step 2(see the circle inside the picture) it looks too complicated i can't help with it i cannot use partial fraction to do because it looks hard to decompose it thank

Hi all. I'm having trouble deciding what I want to do first. I know I can become an RN in two years, which would give me solid opportunity to help people and a laundry list of jobs I would be qualified for... This would give me good stability while I continue to do my schooling, and I imagine...

Hi everyone, Can you tell me how to integrate the following equation? Integrate(1/(x(1+x^2)^0.5) dx

Homework Statement So while doing arc length integrals I can't figure out how to solve them. For instance: f(x) = 3x^2 f'(x) = 6x So.. the length, L = ∫ √(1+36x^2) dx How do you solve this indefinite integral? Notice: I know you can solve this easily with bounds by approximation but how do...

I would like to integrate w.r.t. x, the rest are constants. This is not homework; it is related to a physics problem regarding single-slit diffraction.

Hello I have a set of data points, with errors (X1 , Y1 +- deltaY1) , (X2 , Y2 +-deltaY2) etc I have the covariance matrix for these bins I want to integrate this set of data points: SUM_i ( Y_i * X_binWidth_i ) How do I combine the errors, taking into consideretation the...

$\tiny{Whitman \ \ \ 8.4.7 }$ $\displaystyle \int x \arctan\left({x}\right) \ dx =\frac {{x}^{2} \arctan\left({x}\right) +\arctan\left({x}\right) - x} {2 } + C$ $\displaystyle uv-\int v \ du $ $\begin{align}\displaystyle u& = x& dv&= \arctan\left({x}\right) \ dx \\ du&=dx& v&...

First part of the question was to work out the integral 1/(y+cos(x)) between x=0 and x=pi/2 by using the substitution t=tan(x/2). Got this to be \frac{2}{\sqrt{y^2-1}}arctan(\sqrt{\frac{y-1}{y+1}}) The next question says HENCE find integral with the same limits of \frac{1}{(y+cos(x))^2} Ive...

When using the double integration method to solve for deflection, do you simplify the integral before integrating or do you just integrate it? When i tried it with simplifying and without simplifying, I get a different value for the constant which results in different answers. For example in...

Homework Statement dv/dt = -βv Integrate to find velocity as a function of time, assume the particle's initial velocity is v0. β is constant v = velocity (not constant) t = time Homework EquationsThe Attempt at a Solution dv = -βvdt ∫dv = -β∫vdt --------> limits of integration for the right...

In my Halliday Resnick Walker book, they derive the equations of kinematics using integrals in a small section after the algebraic derivation. I'm extremely confused by the calculus, however. Sorry if my questions are unclear.They say that \frac{dx}{dt}=v⇒dx=v\cdot dt. This first step itself...

Homework Statement Okay, I don't actually have a homework problem that explicitly tells me to find the reason why; it's just something I was wondering while I was trying to integrate circles using trigonometric substitution. But just for reference's sake: "Why does Acircle = ∫√(a2-x2)dx?"...

I have a PDE which is the following: $$\frac {\partial n}{\partial t} = -G\cdot\frac {\partial n}{\partial L}$$ with boundary condition: $$n(t,0,p) = \frac {B}{G}$$ , where G is a constant, L is length and t is time. G and B depend on a set of parameters, something like $$B = k_1\cdot C^a$$...

Homework Statement ∫(1+(1/x))^x dx Homework Equations How do I integrate this compound interest e approximation The Attempt at a Solution Inside: x + ln(|x|) + C Outside: (a^x)/(ln(a))

Homework Statement the correct solution is ∫ tan²x sec²x sec²x dx = replace the first sec²x with (tan²x + 1): ∫ tan²x (tan²x + 1) sec²x dx = expand it into: ∫ (tan^4x + tan²x) sec²x dx = let tanx = u differentiate both sides: d(tanx) = du → sec²x dx = du substituting, you...

What methods are available for integrating, e.g. \int^{\infty}_{0} f(x) dx \int^{x}_{0} g(x,y) dy numerically without resorting to symbolic integration. Thanks

Homework Statement Find the arclength of the curve x = ⅓(y2+2)3/2 from y=0 to y=1. Homework Equations (Please forgive the crazy definite integral symbols - I'm taking a LaTex class tomorrow so hopefully I'll be able to communicate more clearly from then on..!) arclength of curve = ∫ab √ (1 +...

I have a question on finding potential for a disc of charge when it comes to the simple integration how does the integral of R'dR'/etc have the R'dR' just disappear? i thought it would then be R^2/2 I am obviously missing something here

So i was playing Kerbal Space Program and decided i wanted to calculate the maximum velocity of my ship. First, I formed this equation. A(t) = M - dm/dt (t) Where A is the amount of fuel at a given time, M is the total mass of the fuel, Dm/dt is the rate of change of the mass of the fuel, and t...

a = 5 / (3s^(1/3) + s^(5/2)) I don't know if I can do partial fractions on this one, or maybe I'm just doing it wrong.

This is the key step to transform from position space Schrodinger equation to its counterpart in momentum space. How is the first equation transformed into 3.21? To be more specific, how to integral Laplacian term by parts?

Hi, could you please help with the integration of this equation: $$\int_{x}\int_{y}\frac{\partial}{\partial y}\left(\frac{\partial u}{\partial x}\right)\,dydx$$ where ##u(x,y)## . From what I remember, you first perform the inner integral i.e. ##\int_{y}\frac{\partial}{\partial...

If i have an equation: h = ½at2 And: 40 = -4.9t2 → 0 = -4.9t2 - 40 If: v = ∫a then how do i find the velocity given acceleration of -9.8 m/s2?

While reading a proof for an integral equation I came across this formula: http://imgur.com/K8RQlOc It was claimed that it can be proven..

I was just wondering about the path an orbiting particle takes when it's center of circular motion also translates. So as to calculate the distance traveled I know I have to get a function that relates velocity with respect to time and integrate it, but I can't doit, I get stuck integrating. I...

I am struggling to find the antiderivative of the following function: f(x)=\frac{J_{0}(ax)J_{1}(bx) }{x+x^{4} } \\ J_{0},{~}J_{1} : Bessel{~}functions{~}of{~}the{~}first{~}kind\\ a, b: constants \\ F(x)=\int_{}^{} \! f(x) \, dx =? Who can help?

I have the following integral: ## \oint_{S}^{ } f(\theta,\phi) \hat \phi \; ds ##Where s is a sphere of radius R.so ds = ##R^2 Sin(\theta) d\theta d\phi ## Where ds is a scalar surface element. If I was working in Cartesian Coordinates I know the unit vector can be pulled out of integral and...

Good Night, Can someone please tell me how to do: ∫ b (dx/dt) ⋅ dx ? Like in the work done by a force which is proportional to the velocity (like drag). I tried to change dx to v dt but couldn´t go much further. Thank you in advance.

Let's say you have an equation like this: dy=f(x) dx2 Would it be possible to integrate both sides of the equation?

Homework Statement How does one integrate u√(1+u^2) du?Homework Equations Forget what u is being substituted for. It doesn't really matter right now. I just need to integrate what is typed above. The Attempt at a Solution I am completely lost and not sure what to do.

I know that if it were 1/(v2+4) then it would be ln(v2+4) but the other v in the numberator is throwing me off, any help would be much appreciated!

Homework Statement ( V1.4 A.4 C1 - (1/V) ) dV = dA / A C1 is a constant, V=f(x), A=.25*pi*(.0222 - x2) I'm trying to simplify the equation into a form with no integrals or derivatives, so I can put it into MATLAB to spit out an expression for V as a function of x. Or is it possible to put all...

Hey guys, So here's the issue I'm faced with. I need to integrate the following by parts (twice): \int d^{3}y\, e^{ik(\hat{n}_{0}-\hat{n})\cdot\vec{y}}\left[ \nabla\times\nabla\times\hat{\epsilon}_{0} \right] And I have absolutely no clue how to approach this. The result I'm meant to reach is...

Hello every body. I'm searching for a solution to integrate the function below but i couldn't find anything suitable yet.I don't know even how to start it ! can anybody help me finding the integral? f(x)=1/(1-A*cosx)^3 Thanks you ...

Homework Statement ∫δ(x3 - 4x2- 7x +10)dx. Between ±∞. Homework EquationsThe Attempt at a Solution Well I don't really know how to attempt this. In the case where inside the delta function there is simply 2x, or 5x, I know the answer would be 1/2 or 1/5. Or for say δ(x^2-5), the answer would...

Hello, I picked up a challenging problem (at least to me) and I'm having difficulties. 1. Homework Statement An object moves in xy-plane from point O = (0; 0) to point A = (1 m; 0) and from there to point B = (1 m; 2 m). All this time when the object moves a force \vec F = ax2\vec i + by\vec...