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The Maple command

int(exp(-z^2*sin(z)^2), z = 0 .. infinity, numeric, epsilon = 0.1e-1);

However, I am not sure if the answer is correct.

evalf(Int(cosh(t)/(cosh((17/15)*t)+cosh(t)), t = 0 .. infinity));


evalf(int(cosh(t)/(cosh((17/15)*t)+cosh(t)), t = 0 .. infinity));



Hi Everybody.


Doing some calculation in quantum mechanics, I stuble on that integral:

I see immediately that the answer is 1/2.  But Maple 18 cannot give an answer other than a limit that he cannot evaluate.  I even try assumption that p and hbar are realcons.  I get infinity.

Any idea?

Thank you in advance for your help.


Mario Lemelin
Maple 18 Ubuntu 13.10 - 64 bits
Maple 18 Win 7 - 64 bits messagerie : téléphone :  (819) 376-0987

Is there a way to solve the following integral completely?


int(int(x^2+y^2, y = -sqrt(2*a*x-x^2) .. sqrt(2*a*x-x^2)), x = 0 .. 2*a)


When I try solving that all I get is the following:



All is well when I calculate it using polar coordinates though:


int(int(r^3, r = 0 .. 2*a*cos(t)), t = -(1/2)*Pi .. (1/2)*Pi)





Why doesn't maple solve the first one completely and is there a way around this?




I have the following d.e.:

I need to change the s variable into a different one, where the new variable is defined by

(the old s shows up in the limit of the integral)

I tried dchange, but it chokes on this as I don't have an explicit representation of s in terms of Theta.

(I know the overall solution as other people smarter than me have solved this a long time ago, but I 'd like to have the derivation to understand it).

Mac Dude

Dear all,

I would like to solve the Fredholm Integral equation, using numerical method.
This is my code.

there is a problem with subs, does not working here.
# Then, we obtain from (9) the coeficient A[n] and B[n].

Then I woulk like to recompute (2), and then compute (1).
# Puting x=m*h, in (1), how can we generate a linear Matrix from (1).


What is the weak solution integral equation for 

du(x)/dx2 -(1+x2 ) u(x)-1=0

Hi there

There seems to be a bug when evaluating elliptic integrals using assuming. Here's an example:



is our integral for some a. Now evaluate the integral using assuming on X in different ways:


INT2:=simplify(value(INT)) assuming X>0, a>0, a<1;

INT3:=simplify(value(INT)) assuming X<0, a>0, a<1;


These give analytic solutions which are different. Now plot them both and compare to the numeric solution




I'm finding that the red curve which should work for X>0 is wrong, while the green one which is for X<0 is ok for X either sign. [blue is the correct answer - numerically!]


Any ideas?

I am trying to produce an animation. Everything seems correct, but the evaluation is taking a very long time. Even after an hour, it still tries to crank out a graph for me. I even tried to truncate the integral!

Here is my code.


z:= x -> 2*(int((sin(2*y)-sin(y))*cos(y*x)*exp(-y^2*t)/y, y = 0 .. 200))/Pi;

animate(plot, [z(x), x = 0 .. 10, y = -.1 .. 2], t = 0 .. 1, frames = 100);


Would could be the problem? 

I am trying to numerically evaluate the following integral


integral to solve


I have currently used the maple commands


int(exp(10*(-2*y^2+y^4))*exp(-10*(-2*z^2+z^4)), [z = -infinity .. y, y = -1 .. 0], numeric)

evalf(int(exp(10*(-2*y^2+y^4))*exp(-10*(-2*z^2+z^4)), [z = -infinity .. y, y = -1 .. 0]))

evalf(Int(exp(10*(-2*y^2+y^4))*exp(-10*(-2*z^2+z^4)), [z = -infinity .. y, y = -1 .. 0]))


but all of them return the integral unevaluated. Any help?


I have the following function:

and I want to calculate it for a certain set of r, theta and t, but when I use subs, the theta variable is also subsituted int the integral's parameters and I get the folllowing result:

I really don't understand why it does that given that there is no issue for the r variable...


Thanks in advance for your help!

P-S: please forgive my poor English : I'm a French student...



int(sin(x)^cos(x),x= 0 .. Pi)

with Maple? A closed-form answer is also welcome.


I'm new here and I couldn't find similar problem in this forum.

I want to use variable (red marked) with unit definite integrals but it doesn't work. I put the file with units and file without units (to check correct solution) in this post.

What to do?




I am trying to create a procedure that can solve integrals using the Composite Simpson's 3/8 rule. However when I test my procedure against maple's ApproximateInt I am getting the wrong results.

Here is my attempt:


f:= x -> exp(x)*sin(4*x); # function I am using

simp := proc(a, b, n)
  local h, sum, i, single:
  h := (b-a)/n:
  sum := 0:
  single := (3*h/8) * (f(a) + f(b)): # this is the end points
    for i from a+h by h to b-h do
       sum := sum + (3*h/8) * (3*f(i)):
    end do:
print(evalf(sum + single));
end proc:

evalf(Student:-Calculus1:-ApproximateInt(f(x), 0..1, method = simpson[3/8], partition=12));



As you can see my answer is not very close to the answer given by Maple. I am not sure why my procedure simp is wrong.

How can I get solution of  the following equation of orbit for schwarzschild BH in form of Jacobi Elliptical Integrals on Maple 12 platform,

diff(r(phi), phi) = r^2*sqrt(e^2-(1-2*M/r)*(1+l^2/r^2))/l

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