# Items tagged with integrationintegration Tagged Items Feed

### 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;)

### Speeding Up Solving Equation Numerically...

January 26 2015
0 4

I am currently running into an issue where the numerical solution to an equation (involving an integral, yes, but the value I am solving for is simly a constant in the integral) is taking significantly longer than I would hope it would to solve. I am solving a similar equation (with a simpler expression) and it is significantly easier to solve, and I am hoping for that kind of speed.

On the last two lines in the attachment, I have two expressions. The penultimate expression is the baseline speed that I would like to match. The last expression is the fsolve I would like to speed up.

Is there any way to numerically speed up the process? I found that when I did tracelast after halting the process, there were HUGE numbers being added and subtracted, multiplied and divided. Not only did this significantly slow down the proecss but it also adds much numerical instability, which I would also like to avoid.

All help would be appreciated.

pole-dragging-mapleprimes.mw

### Numerica multiple integration...

January 24 2015
1 11

Hi, all

I use INT to calculate multiple integration as below. It runs more than 20 hours without results. I wander is there any problem in my codes.

restart;
A := sin(k*Pi*(x-h*cos(theta))/a)*sin(l*Pi*(y-h*sin(theta))/b)*sin(k[0]*h)*sin(k*Pi*x/a)*sin(l*Pi*y/b);

W := evalf[5](int(int(int(int(A, h = 0 .. (x-a)/cos(theta)), theta = Pi+arctan((b-y)/(a-x)) .. 3*Pi*(1/2)), x = 0 .. a), y = 0 .. b, numeric))

Thanks

### Error, (in IntegrationTools:-Combine) invalid subs...

January 04 2015
1 4

according to help on Combine

The Combine command combines integrals using linearity. The parameter v is any expression involving definite or indefinite integrals.

So, why I get an error from the following?

restart;
expr:=Int(sin(x),x) + Int(cos(x),x);

IntegrationTools:-Combine(expr);

Error, (in IntegrationTools:-Combine) invalid subscript selector

interface(version);
Standard Worksheet Interface, Maple 18.02, Windows 7, October  20 2014

### Integral of natural logarithm finction...

December 16 2014
0 4

Hello everyone,

I'm using Maple18, I tried to integrate the function including natural logarithm:

Is there any simple way to directly convert the answer to the kind of form we want? I cannot not finish the conversion:

So the toolbox "IntegrationTools" was used, but finally, we couldn't compute the integral:

However, we can get the correct answer by manually inputting the formula.

Using IntegrationTools is pretty nasty and not very convenient, such as the problem I mentioned.

Does anyone have another solution?

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