MaplePrimes - Questions and Posts tagged with integral

Integrate density of states times Fermi distribution over energy

mzh — Mon, 07 May 2012 21:14:50 Z

Dear Maple Users

Let the density of electronic states be denoted

Question for solving integral?

Alaza — Sat, 05 May 2012 14:53:29 Z

Hi there,

I am trying to find an analytical solution to an integral. Unfortunately, I only get the function call returned. Is there anything I can do to get Maple to solve it?

Thank you

integral_question.mw

Integral function with variable upper limit

styie — Sun, 29 Apr 2012 13:00:34 Z

E := proc (phi) options operator, arrow; int(1/(1-(1-1/kappa^2)*sin(phi)^2)^(1/2), phi = 0 .. phi) end proc

E(pi/2)

Is there a way to get this function to work properly without having to simplify the integral manually ?

kappa is a constant (with a value of 12.4)

Thanks in advance!

hypergeom and integral

goli — Tue, 24 Apr 2012 04:43:08 Z

Dear guys

To solve a typical integral I have written

int((t^(f-3/2))*(1-t^(2*(f-1)))^(-1/4),t);

but the solution is very complicated and contains "hypergeom". How can I have a simpler solution? I mean an explicit solution.

Thanks.

Too long an ODE?

mgu — Sat, 07 Apr 2012 03:54:21 Z

I have an ODE to solve that looks like this:

((diff(R(r), r, r, r, r))*r^4+3*(diff(R(r), r))*r-3*(diff(R(r), r, r))*r^2+2*(diff(R(r), r, r, r))*r^3-3*R(r)+4*R(r)*n+2*R(r)*n^2-4*(diff(R(r), r))*r*n+2*(diff(R(r), r))*r*n^2+4*(diff(R(r), r, r))*r^2*n-2*(diff(R(r), r, r))*r^2*n^2-4*R(r)*n^3+R(r)*n^4)/r^4 = (-108-1362*n+2122*n^2+2019*n^3-3032*n^4+401*n^7+1192*n^6-1033*n^5-25*n^9+6*n^10-180*n^8-4128*r^(n+3)*n^3+2304*r^(n+3)*n-576*r^(n+5)*n-760*n^6*r+575*n^5*r-244*n^7*r-2108*n^3*r-11616*r^(n+3...

problems about displaying the mathematics symbols

521dada — Fri, 30 Mar 2012 07:33:52 Z

First,a Maple file is exported as the html file,but it took too much time to load the applet(com.maplesoft.applets.MathMLViewer)to display the mathematical symbols,such as the symbols of integral and differential,as shown in Figs.1 and 2.How to accelerate
loading rate of Java applet?
Second,the problem will occur in the browsers of IE and firefox that the equation is incomplete display as shown in Figs3.Is there a method can handle the problem?
The last,using the...

Integral over a vector

mah00 — Sat, 24 Mar 2012 23:31:00 Z

Hi everyone,

Is it possible to perform an integral over vector without writing a multiple integral over each component?

I am integrating over a vector of dimension 12, so I am trying to find another way to calculate rather than writing 12 integrals.

Thanks

Bug in integrals of absolute value

Doug Meade — Tue, 20 Mar 2012 14:30:00 Z

A common example to emphasize that it is not OK to bring absolute values inside the integral compares

abs( int( cos(n*x), x=0..Pi ) ) asuming n::integer

and

int( abs( cos(n*x) ), x=0..Pi ) assuming n::integer

Maple correctly formulates the first to 0. But the second expression gives it more trouble, returning two messages:

Warning, unable to determine if (1/2)*Pi*(1+2*_Z7)/n is between 0 and Pi; try to use assumptions or use the AllSolutions option
Warning, unable to determine if (1/2)*Pi*(1+2*_Z8)/n is between 0 and Pi; try to use assumptions or use the AllSolutions option

How to Find Optimum Value

poyan200 — Thu, 15 Mar 2012 21:18:15 Z

Hello

I have an equation of power (P)with 3 variables. The variables are R (resistance), ω (frequency) and K (spring stifness);

I would like to find out the optimum value of R and K to maximize the comulutive value of power when the ω is varying from ω1 to ω2. To do so, I should do the following steps:

Step 1: Calculate the integral of Power when ω is changing from ω1 to ω2 : U(R,K...

How do I input the integral?

toandhsp — Tue, 13 Mar 2012 04:20:39 Z

How do I input the integral?

int((x-m^2)/(x+1),x=0..m^2).

Please help me. Thank you.

Obtaining an analytical solution for a specific integral

ntnu — Wed, 08 Feb 2012 11:13:56 Z

We are trying to obtain an analytical solution of an integral in Maple. When solved numerically the integral converges, but we are not able to get an analytical solution. Any ideas?

The constants in the integral is computed independently, not sure if knowing them can help. The values are r=0.06, kappa=2.6, myksi=2.18, rho=-0.21, stdk=382.2, stds=47.8, kji=52.9 and ksi=62.3. We kind of need the analytical solution to handle the expression in further calculations, and...

Hyper geometric functions

amrramadaneg — Sat, 28 Jan 2012 11:00:21 Z

Hi,  I have and integral its results contains Beta function and hypergeometric function.
I found a difficulty to program the hypergeometric function with Maple 13.    is any one can solve this problem
where

∫₀^{(π/2)}((sin^{α}xcos^{β}x)/(√(1-k²sin²x)))dx=(1/2)B(((α+1)/2),((β+1)/2))F(((α+1)/2),(1/2);((α+β+2)/2);k²),α>-1,β>-1,∣k∣<1

The problem in written...

Getting a weird result with integration of an absolute value

TommySnowman — Mon, 16 Jan 2012 16:33:18 Z

I'm working on a simple toy model as an introductory example to some work I am writing up. I was hoping the example would be simple enough to get some nice analytical results to write up. However, maple is giving me some odd results.

Essentially I have taken the integral of the absolute value of an error that I have caluclated which has given me a somewhat nonsensical result. The attached file contains the specifics (hopefuly it's visible)...

How to work out this integral

gxljx — Tue, 03 Jan 2012 21:50:08 Z

How to work out this integral

Any way to reclaim NAG (_d01akc) allocated memory ?

Louis Lamarche — Fri, 09 Dec 2011 17:30:02 Z

I am evaluating a difficult integral of an oscillating function.

f:=k->evalhf(piecewise(k=0,1,k>0,cos(k*(dz))*BK0(k*rho1)/BK0(k*a)));

evalf(Int(f, kmin..kmax, method = _d01akc,epsilon=eps,maxintervals=1000000))

with dz>0 and possibly very large
kmin is Pi/(2*dz)
the number of cycles is nc = ceil((1/2)*kl*dz/Pi) with kl = 91.563
kmax= kmin+nc*2*Pi/dz

Each evaluation of this integral using a call to the NAG routine (_d01akc ) eats up