# Items tagged with integralintegral Tagged Items Feed

### Maple gives wrong results?...

Yesterday at 10:45 PM
3 14

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

5.210624833

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

2.720144439

### An integral that cause probel with Maple...

April 13 2014
0 5

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?

--------------------------------------
Mario Lemelin
Maple 18 Ubuntu 13.10 - 64 bitsMaple 18 Win 7 -  64 bits
messagerie : mario.lemelin@cgocable.ca
téléphone :  (819) 376-0987

### Solving integral containing unknown values...

April 11 2014
2 1

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:

$\int_{0}^{2a}(2x^2)\sqrt{2ax-x^2}+\frac{2}{3}(2ax-x^2)^\frac{3}{2}dx$

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)

=         $\frac{3}{2}a^4\pi$

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

Thanks

Calor

### A problem with dchange...

April 10 2014
0 4

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

### Integral equation: problem in the code, subs...

April 10 2014
0 2

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).

Fred.mw

Thanks

### What is the weak solution?...

April 06 2014
0 1

What is the weak solution integral equation for

du(x)/dx2 -(1+x2 ) u(x)-1=0

### Problem with elliptic integrals and assuming...

April 01 2014
0 6

Hi there

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

INT:=Int(1/sqrt(a*x^3+1),x=0..X);

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

plot([subs(a=0.1,INT2),subs(a=0.1,INT3),subs(a=0.1,INT)],X=-1..1,colour=[red,green,blue]);

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?

### Animating an integral...

March 21 2014
3 10

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.

with(plots):

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?

### Numerical integration...

March 21 2014
1 4

I am trying to numerically evaluate the following integral

$\int_{-1}^0\int_{-\infty}^y&space;e^{10(-2y^2+y^4)}e^{-10(-2z^2+z^4)}dzdy$

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?

### Problem when using subs on an double integral...

March 17 2014
0 2

Hi!

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...

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

Florent

### How to find the integral...

March 08 2014
1 21

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

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

### Problem with units in definite integral...

March 02 2014
1 4

Hi,

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?

Files:

01_referat(without_u.mw

### Composite Simpson's 3/8 Rule...

February 18 2014
1 3

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:

restart;

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:

simp(0,1,12);
0.6224486445
evalf(Student:-Calculus1:-ApproximateInt(f(x), 0..1, method = simpson[3/8], partition=12));

0.5323516717

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.

### jacobi elliptical integrals...

February 10 2014
1 4

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

### Differential equations but with upper and lower bo...

February 03 2014
1 2

In a trivial example of where x goes from 0 to 1 of d n(x)/dx =a, where n(0)=1, n(1)=2, so that the integral is solved easily, how can i do this in maple however I can only solve an eqation with the initial condition, if i try anything else then i get errors such as,

fx := diff(n(x), x)-a

A := rhs(dsolve({fx, x = 0 .. 1, n(0) = 1, n(1) = 2}, n(x)));

Error, (in dsolve) invalid terms in sum: 0 .. 1

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