# Items tagged with integrationintegration Tagged Items Feed

### Integration with Units Error...

7 hours ago
3 6

This is my first attempt at trying the units feature within Maple. I have had mixed results. I have a function defined that gives me values in [cal/mol/K], which is correct. But when I try to use this as the integrand in an integral definition it does not want to solve. I cannot determine what the problem is.

I thought that I possibly needed to define units in the integral expression, but this just produces more errors or locks-up Maple completely. (Side note: When Maple locks-up, the "interupt current operation" toolbar often does not correctly kill the operation, and I am forced to restart Maple :/)

As I have the problem defined, I should get the following result:

T__sys= 64.47487 [K], should get me HIG(T__sys) = -19682.7 [cal/mol].

See attached: EnthalpyTrace_-_Integrating_with_Units_Error.mw

Any help or insights would be greatly appreciated.

### How do I perform numerical integration on an array...

August 18 2015
2 10

I have an arrays of data. One for x values, and one for y values. How can I obtain a numerical integration of y for a range of x values?

I have tried defining a function of X using ArrayInterpolation(x,y,X) and then calling evalf(Int(f,xmin..xmax)) but that gives an error message. (I don't seem to be able to paste into this window) The error message says

"Error, invalid input: evalf expects its 2nd argument, n, to be of type posint, but received numeric."

I thought I was using a form of the equation right from the help system.

I also tried the 2D version of integration, but it returns the difference of my limits times my function name.

I aslo tried AdaptiveQuadrature, but I can't get that to work either.

-Mike McDermott

Newbie Maple user

### Symbolic Integration...

August 17 2015
3 11

Just trying Maple again after 10+ years, so please bear with me. I am basically trying to do a symbolic integration, where the output should be the antiderivative of the function I am integrating. However, I have not been able to succesfully get the output I expect.

I defined a function Cp(T), with constants C1, C2, etc. like so:

C__p := T -> C__1+C__2(C__3/(T*sinh(C__3/T)))^2+C__4(C__5/(T*cosh(C__5/T)))^2

But when I integrate the function using int(Cp(T), T=Tref..Tsys) it does not output the antiderivative as I would expect. This is what I am looking for, but it just gives me the equation within the integral sign without symbolically solving integral. Can this be done?

It should be,

int(Cp(T), T=Tref..Tsys) = C1*(T2-T1) + C2*C3[coth(C3/T2) - coth(C3/T1)] - C4*C5[tanh(C5/T2)-tanh(C5/T1)]

Trivial integrals such as int(x2,x) = 2x solve okay, so I am assuming I setup the problem incorrectly. I just cannot figure out what I did wrong, and it is driving me crazy. I already wasted more time than is healthy on this. Any help would be greatly appreciated. Thanks.

### difficult integration from zero to infinity...

July 25 2015
0 5

restart; with(LinearAlgebra); int(exp(-(ln(z/(snr*B^2))+4*sigma^2)^2/(32*sigma^2))*eta^2*(y/z)^((1/2)*eta^2-1)/(z*sqrt(32*Pi*sigma^2)*(2*sqrt(y*z))*(2*A[o]^(eta^2))), z, z = y/A[o]^2 .. infinity);

restart; with(LinearAlgebra); int(exp(-(ln(z/(snr*B^2))+4*sigma^2)^2/(32*sigma^2))*eta^2*(y/z)^((1/2)*eta^2-1)/(z*sqrt(32*Pi*sigma^2)*(2*sqrt(y*z))*(2*A[o]^(eta^2))), z, z = y/A[o]^2 .. infinity)

### a few integrals in Maple...

June 13 2015
1 6

Trying a few integrals in Maple -- doesn't seem to handle them very well. Any workarounds please?

f1(p,b):= 1/(p^2 + b^2)^2 ;

f2(p,b):= exp(-p/b)^2;

T1pbm := Int(q*f1(q, b)*ln((p+q)^2+m^2), q = 0 .. infinity);

T2pbm := Int(q*f1(q, b)*ln((p-q)^2+m^2), q = 0 .. infinity);

with(IntegrationTools):

PT1 := evalf(Parts(T1pbm, q*f1(q, b), ln((p+q)^2+m^2)));

PT2 := evalf(Parts(T2pbm, q*f1(q, b), ln((p-q)^2+m^2)));

Ev := evalf(-pi*c*Int*(p*f1(p, b)*(PT1-PT2), p = 0 .. infinity))

### Integarion of function...

June 04 2015
1 4

hello all.

trying to integrate sach equation:

Fun := Diff(f(x), x);

int(Fun, x = 2 .. 7);

waiting that maple give my something like this f(7)-f(2). But it write only integration form.

What i need to have f(7)-f(2)?

Thanks.

### How to speed up numerical integration...

June 02 2015
0 2

Hello all.

Need help.

My project are too slow calculate integrals. What can i do to speed up numerical integration?

Thanks all.
MP_1.mw

June 01 2015
0 5

Int(ln(1+sqrt((x+1)/x)),x);

value(%);

Does not work.

Int(ln(2+sqrt((x+1)/x)),x);
value(%);

Works.

But with some effect,

Could this possibly be improved in the next release?

### Integrating an equation with unknown constants....

May 05 2015
1 2

This might seem easy but i am a total beginner in Maple and i really need to know how to do this. If i have an expression like this:

X^2 + 3*y + 3*z + X^7

where (y) and (z) are constants of unknown values. I need to integrate the expression over an interval for example (from 1 to 10) so that the answer would still be in terms of (y) and (z).

### A maple/maths question to be answered by YOU ;-)...

May 01 2015
2 10

$\int_{a}^{b} f(x) \, dx \approx \tfrac{3h}{8}\left[f(x_0) + 3f(x_1) + 3f(x_2) + 2f(x_3) + 3f(x_4) + 3f(x_5) + 2f(x_6) + ... + f(x_n)\right] .$

A Fantastic Good morning Ladies and Gentelmen,

You have the mission to find the problem in that code/ give a better code?
I want to write a procedure for the simpson 3/8 rule using the above formula I took from wikipedia :
(I don't want to use any super maple command that estimate the simpson 3/8, but just using this formula and starting from scratch, I am a beginner so feel free to laugh at my code hehehe)
here is the code I managed to write after 365 hours :D

restart:
simp38:=proc(f,x0,xn,n)
local h,summ,i,x,Integral:
h=evalf((xn-x0)/n);               #h is the distance between 2 points
summ:=f(x0)+f(xn);              #initialise the summ

for i from 1 to n-1 by 3 do
x[i]:=x0+i*h:
summ:=evalf(summ+3*f(x[i])):
od:
for i from 2 to n-1 by 3 do
x[i]:=x0+i*h:
summ:=evalf(summ+3*f(x[i])):
od:
for i from 3 to n-1 by 3 do
x[i]:=x0+i*h:
summ:=evalf(summ+2*f(x[i])):
od:

Integral:=3*h/8*summ;
end:

simp38(x->(x^5-5.15*x^2+8.55*x-4.05045),1,5,6);   #testing it      --->2481.087090
evalf(int(x^5-5.15*x^2+8.55*x-4.05045,x=1..5));      #comparing it --->2477.531533

### An unknown error int command to use...

February 19 2015
2 4

Hi number of officials,

As I enter the command defined 'int' I get an error message.

What can I do. Can you help me.

Commands Entered:

int(x^2+3*x, x);

ansvers:

Error, (in int) wrong number (or type) of arguments: invalid option value passed to indefinite integration: {}

### posterior plot animation...

February 15 2015
0 4

Greetings, seeking an expert to animate a plot.

see worksheet.posterior_graphs_(encapsulted)_1D.mw

before they play each other, each have a law (a normal distribution) plot-output 6.

after DD defeats CC, and a numerical integration is performed the new laws are given by plot-output 18.

as you can see, the laws of DD and CC are closer together.

if the calc was repeated (DD defeats CC again), the laws would be closer again.

so what i require is an animation of the new laws from game 1 to (say) game 6 (DD defeats CC every time). seeing the red and blue distributions merging would be ideal.

as an aside I heard maples FFT could simplify the complicated integration. any suggestions?

cheers

### four dimensional integration...

February 14 2015
1 1

Hi,

I am trying to discretize a kernel of the form $K(x,y,t,s)$. I want to evaluate a four dimensional integral of the form

\int\int\int\int K(x,y,t,s)*h_m(x)*h_n(y)*h_p(t)*h_q(s) dsdtdxdy, where limits of integration are from 0 to 1.

$h_m()$ are function of one variable.

please suggest how to evaluate this.

thanks

### How do i solve integration of odes using composite...

February 13 2015
1 5

hai everyone. i am currently trying to solve an integration of the following ∫g(η)dη . integrate from 0 to 10.

from the following odes.

f ''' +1-(f ')2 +ff ''=0,

g''-gf'+fg'=0,

with boundary conditions f(0)=0, f'(0)=λ, f'(∞)=1, g(0)=1,g(∞)=0

First, i solve the odes using the shooting method. then i used the trapezoidal rule to solve for the integration of g(eta) using the following codes

> with(student);
> trapezoid(g(eta), eta = 0 .. 10, 10);
> evalf(%);

it seems that it can not read the data from the shooting method. can anyone suggest why it is happening?

thank you verymuch for your concern :)

### maple 18 does not integrate...

February 01 2015
1 3

Hello everybody!

My name is Mathew and I am a new member of this forum, and this is my first post, so please be lenient towards me:) I wanted to ask for help since my adventure with Maple 18 was supposed to start yesterday, unfortunately I encountered a problem I couldn't solve myself so far- my Maple 18 does not integrate. At all. It has no problem with differentiating, adding, subtracting and such, unfortunately any type of integral is unsolvable by Maple. I tried typing the easiest functions, such as e2xdx under the integral, unfortunately it is met with following message:

Error, (in int) wrong number (or type) of arguments: invalid option value passed to indefinite integration: {}.

I understood from several tutorials on the internet that this program should not have any problems with dealing with such form of formulas. What could be wrong? How to make  it work as it is supposed to?

Please help me. As I mentioned in the beginning, I am a new member, so in case I did something wrong or placed this post in wrong category- please forgive me;)

 1 2 3 4 5 6 7 Last Page 1 of 11
﻿