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Hello;

I need some help to compute the limits of integral:

 

and

 

Thank you for your help.

 

I_Mariusz

limity.mw

Hello All.

Why Maple can’t do this Simple indefinite integral?

I'm have a integral :

 

Please compare to Mathematica:

Thanks in advance for your help.

 

I_Mariusz

test.mw

After manually working out answer for problem 4-4 in Mathews & Walker's Mathematical Methods of Physics , I tried to check my solution with maple2015. Briefly the problem involves inputs periodic with period T, being transformed into outputs, through a kernal G.  The net result is that all input frequencies omega periodic in T are multiplied by (omega_0/omega)^2, except for constant frequency which transforms to zero.  The problem asks to evaluate the kernal G.

Maple2015 correctly evaluated the integral for a constant input, a cosine input, and a sine input, but gave undefined when I tried an exponential(i*x) input which is just a linear combination of the two previous inputs.  I found this interesting because the integral is finite, well defined, and only has an absolute function (in the kernal), which may cause Maple problems, as it correctly evaluated integral when I split it into two regions.  Interestingly if instead of working with a period of T, I used 2*pi, and redfined my G function accordingly, Maple evaluated the exp input integral without any problems.  So the problem appears to be with the T variable, but I correctly used assumptions of T>0, and 0<t<T, so I am not sure why it would work correctly when I use T=2*pi, but failed when using a general period T.  Any help would be welcome.

 

 

restart

assume(T > 0)

assume(0 < t and t < T)

about(T)

Originally T, renamed T~:

  Involved in the following expressions with properties
    T-t assumed RealRange(Open(0),infinity)
  is assumed to be: real
  also used in the following assumed objects
  [T-t] assumed RealRange(Open(0),infinity)

 

about(t)

Originally t, renamed t~:

  Involved in the following expressions with properties
    T-t assumed RealRange(Open(0),infinity)
  is assumed to be: RealRange(Open(0),infinity)
  also used in the following assumed objects
  [T-t] assumed RealRange(Open(0),infinity)

 

assume(n::integer, n > 0)

about(n)

Originally n, renamed n~:

  is assumed to be: AndProp(integer,RealRange(1,infinity))

 

G := proc (x) options operator, arrow; (1/2)*omega0^2*T^2*((1/6)*Pi^2-(1/2)*Pi*abs(2*Pi*x/T)+Pi^2*x^2/T^2)/Pi^2 end proc

proc (x) options operator, arrow; (1/2)*omega0^2*T^2*((1/6)*Pi^2-(1/2)*Pi*abs(2*Pi*x/T)+Pi^2*x^2/T^2)/Pi^2 end proc

(1)

(int(G(t-tp), tp = 0 .. T))/T

0

(2)

(int(G(t-tp)*sin(2*Pi*n*tp/T), tp = 0 .. T))/T

(1/2)*T^2*omega0^2*cos(t*Pi*n/T)*sin(t*Pi*n/T)/(Pi^2*n^2)

(3)

(int(G(t-tp)*cos(2*Pi*n*tp/T), tp = 0 .. T))/T

(1/4)*T^2*omega0^2*(2*cos(t*Pi*n/T)^2-1)/(Pi^2*n^2)

(4)

(int(G(t-tp)*exp((I*2)*Pi*n*tp/T), tp = 0 .. T))/T

undefined/T

(5)

(int(G(t-tp)*(cos(2*Pi*n*tp/T)+I*sin(2*Pi*n*tp/T)), tp = 0 .. T))/T

undefined/T

(6)

simplify((int(G(t-tp)*exp((I*2)*Pi*n*tp/T), tp = 0 .. t))/T+(int(G(t-tp)*exp((I*2)*Pi*n*tp/T), tp = t .. T))/T)

(1/4)*omega0^2*exp((2*I)*t*Pi*n/T)*T^2/(Pi^2*n^2)

(7)

assume(0 < t and t < 2*Pi)

G2 := proc (x) options operator, arrow; 2*omega0^2*((1/6)*Pi^2-(1/2)*Pi*abs(x)+(1/4)*x^2) end proc

proc (x) options operator, arrow; 2*omega0^2*((1/6)*Pi^2-(1/2)*Pi*abs(x)+(1/4)*x^2) end proc

(8)

(int(G2(t-tp)*exp(I*n*tp), tp = 0 .. 2*Pi))/(2*Pi)

omega0^2*exp(I*n*t)/n^2

(9)

 

Download MathewsWalkerProblem4-4.mwMathewsWalkerProblem4-4.mw

 

 

I hoped that Maple would return the value of 1 in all commands (see below). However, introducing a scaling parameter, sigma, yields the unevaluated expression. Why? I still think it should evaluate to the value of 1.

 

kind regards,

Harry (not a mathematician, but a psychologist)

 

 

 

integral.mw

Hi,

 

I am trying to evaluate an integral and expecting an expression as a result. But the following code does not provide expression.

 

I am geting

 

I need help.

 

Thanks.

 

 

 

Compute the following multiple integral exactly and/or with 10 correct significant digits

Int(  exp( - add(x[i],i=1..10)^3),  seq(x[i]=0..1, i=1..10) );

  The problem is suggested by a previous post.

Hello,

 

I'm trying to solve the integral u/(1-u) with Maple and noticed that it returned a result that doesn't accord to the solution I found by hand or the solution from WolframAlpha. This is a screenshot of the weird behaviour:

Does Maple do any weird conversions? Or did I do something wrong or is Maple wrong?

Thanks in advance,

Hello people in mapleprimes,

I have a question about how Int does.

The following function spy returns 0, of course, with a side effect of listing the value of x one by one to secrets.

secrets := NULL:

spy:=proc(x::{name,numeric})
  global secrets;
  if type(x,name) then
    return 'procname'(args)
  else
  secrets:=x,secrets;
  return 0;
  end if;
end proc;

 

And, with this function, calculation of the Int, that is, following brings a sequence of numbers:

evalf(Int(spy,0..1));

secrets;

.7506605773, .2493394227, .9118140517, 0.881859483e-1, .9970470440, 0.29529560e-2, 1.0000000000, 2.2449529449*10^(-11), .5000000000

 

The question I have is why the number of this sequence is not from smaller( or greater) to greater (smaller) in order,

but in random order. And, numerical calculation of Int can be done with only 9 points extracted?

 

Best wishes.

taro

 

 

 

 

 

How evaluate system of two integral equation by laplace transform ?

 

with(inttrans):

L := laplace((1/2)*x^2+(1/2)*x^3+(1/12)*x^4 = int(u(t)*(-1+x-t)+v(t)*(1+x-t), t = 0 .. x), x, s);

(s^2+3*s+2)/s^5 = laplace(int(u(t)*(-1+x-t)+v(t)*(1+x-t), t = 0 .. x), x, s)

 

(3*s^2-s+2)/s^5 = laplace(int((1+x-t)*u(t)+(-1+x-t)*v(t), t = 0 .. x), x, s)

(1)

``

 

Download Qu_2_mapel.mwQu_2_mapel.mw

How to evaluate The Abel integral has the form I can not compute this

> restart;

> f := proc (x) options operator, arrow; (4/3)*x^(3/2) end proc; k := proc (x, t) options operator, arrow; 1/sqrt(x-t) end proc;

> int((4/3)*t^(3/2)/sqrt(x-t), t = 0 .. x);

Thank you :)

 

> restart;> f := proc (x) options operator, arrow; (4/3)*x^(3/2) end proc; k := proc (x, t) options operator, arrow; 1/sqrt(x-t) end proc;> int((4/3)*t^(3/2)/sqrt(x-t), t = 0 .. x);

 

Hi there, I am a new user of Maple. I am trying to use intsolve for a course project requiring solving an integral equation. I saw Maple has the intsolve function, then I bought it. However, it didn't seem to work for me.

I typed s(x) and r(y) in and try to solve this problem.

 

 

 

It took 20 minutes; it's still evaluating... what should I do?

Hello Please, I was wondering if I can get this equation solve either in closed form or approximate form:

 

mu = theta*beta^a*(int(t^a*exp(-beta*t)/(-lambda*t+1), t = 0 .. infinity))/Gamma(a)

 

 

Many thanks 

There are dozens of indefinite integral expressions in my worksheet. Everytime I execute the entire worksheet, the cursor always rests beside one indefinite integral expreesion and Maple stays in "Evaluating...". Even 30 minutes passed, the result of the integral couldn't come out. What bothers me is that the cursor would rest beside different indefinite integral expressions. For example, I write 4 indefinite integral expressions A, B, C and D one by one. First time, the results of A, B and C come out and the cursor rests beside D with "Evaluating...". Next time, the results of A and B come out and the cursor rests beside C with "Evaluating...".

Before the indefinite integral expressions, I wrote dozens of lines of codes aiming at assigning values to variables. As I typed more and more indefinite integral expressions into the worksheet, even evaluating the codes aiming at assigning values would spend more and more time.

Does Maple evaluate the codes line by line from the top to the end of a worksheet? If it is true, why evaluating the codes before the indefinite integral expressions becomes slowly?

How to evaluate the entire worksheet without stuck in one indefinite integral expression?

How to get the approximation of definite integral if explicit integral could not be found?

explicit_integral_could_not_be_found.mw

If explicit integral could not be found, is there any function or method to get the approximation of a definite integral?

Another_way_to_calculate_the_definite_integral.mw

ptin the file I upload is a complicated expression containing θ and r. Will the accuracy of the result be affected if I use the second method in the file to calculate the definite integral?

 

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