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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...

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...

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

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 

I have the numerical solution of Phi(r,t) which is a numerical solution of a pde..

I want to find the following energy integral at fixed time say t=10 ,

Energy = int(a*r^2*Phi(r,10)^2 + 2*b*r*Phi(r,10)^3,r=0..infinity)... I could not find help in maple.. I guess I had to do the following

1. select the numerical solution dependent only on r at t=10 slice..

2.Use numerical methods to evaluate the integral..

I ‘d like to compute something as follows at certain r and z, but first I must compute the integral and then substituting the r and z values.

A(r, z) = int( f(r,z, teta), teta=0..0.78)

But the problem: f is a complicated function of the 3 variables (including BesselJ(0,..), sin & root square functions, ..!!) thus a simple int command...

I've just registered my copy of maple and I'm trying to figure out how to use it to find the arc length of a curve on a given integral. My function is: upper limit 0, lower limit -3; and after the integral sign, the square root of 1+4x^2 dx.

-JerJohn123

Hi.

I have defined a function "norma" that calculates the normal vector in a point "r" in a given surface:

norma:=proc(l,r) local nu;

if r[1]>= l/2 then nu:=[r[1]-l/2,r[2]];

elif r[1]<=-l/2 then nu:=[r[1]+l/2,r[2]];

...

Now I need to calculate an integral using this function varyign the parameter "r" but I get this error message:

> int(norma(l,[cos(x), sin(x)]), x = -1.5768 .. -.5638);
Error, (in norma) cannot...

How to calculate the integral
restart; int(cos(a*x)*cos(x)^(a-2), x = 0 .. (1/2)*Pi) assuming a>1
with Maple? Mathematica 8.01 produces a very doubtful answer
In[1]:=Assuming[a > 1, Integrate[Cos[a*x]*Cos[x]^(a - 2), {x, 0, Pi}]]
Out[1]=((-1)^a* a* HypergeometricPFQ[{1, 1 - a, 1 + a}, {3/2, a}, 1/2]* Sin[a *[Pi]])/(-1 + a)

Dear Dr. Lopez,

I would like to make a visualization of the following:

y=0.9       0 <= x <=4

y=1-0.1e^(-0.1x)   4<x

z=1

Please help. Thank you very much.

Sincerely,

Giao Che

Dear guys!

I'm solving an equation and then by its results I solve an integral, but I'm doing that for many initial conditions in a for loop. The problem is that when I change the limits of loop (or initial conditions) the result of integral in two for loop for a same initial condition are very different. What's the problem?

Thanks!

Hey guys,

I have the function f(x) =(sin(x) + 1)/(x^2 + 1) where x =-Pi/2 and 3Pi/2

1) I first set up an intgral for the function:

Dear guys! I'm solving a system of ODEs in a for loop with different initial conditions and after that in each loop I use the result to solve an integral and after all I find the minimum value of integrals. But the problem is that when I write for loop with for example 100 initial conditions I get a result and when I expand the numbers to for example 1000 initial conditions where include the 100 previous one maple tell me that the initial conditions that make the integrel minimum are the same ...

Dear guys! I'd like to know that for solving an integral by maple we have to use " int " or we have any other choices? Because I have an integral with large limits from 0 to for example 1000 and it takes much time for maple to solve it.