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Hello,

I have a maple code, which some expressions have more that 80000 terms and I need to double integrate them. The terms have sine, cossine trigonometric functions.

I tried to used de MAP command, it works for the first expressions but, after a while, Maple displays an error message related to too large expression.

Do you know how to handle large expressions ?

Thank you.

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?

 

Hello, i am doing some schmidt-analysis on a stirling engine, but my question is rather simple. I have the measured presure P at a given time T as a 229x2 matrix, i also have a function, V__total(T), for the total volume of the engine at a given time T. 

I then go on to create a pointplot PV, which is rougly the shape of a potato. I now want to find the area enclosed by this point plot, is there any way? 

I do something like:

> DATA:=ImportMatrix(filepath,skiplines=1); %import data from .txt file, skip header line. 

>P:=DeleteColumn(DATA,1); %Isolate presure column

>T:=DeleteColumn(DATA,2); %Isolate time coliumn

>V:=V__total~(T); %Generate volume vector as a function of time T

>pointplot(<P|V>,connect=true);

Is there any wat to finde the area enclosed by the curve/ Int(P,V)

This is the code example_hw2.mw which derives from hw2_I1.mw.

hw2_I1.mw works but example_hw2.mw doesn't work and the differences between two codes are two new function I added to the dsolve which are η(t) and I2(t). The I2(t) is the second part of I1(t) at the interval t>t* which subject to Phi(t*)=0.

So how to make the sentence 'if |(H(t))/(omega)|>1 then eta(t)=0 else eta(t)=arccos(-(H(t))/(omega))' and 'I2(t) = (int(p(t), x = -eta(t) .. eta(t)))/Pi' work?

 

I have in mind

.

My unsuccessful trials are

evalf(Int(cos(log(x)/x)/x, x = 0 .. 1, method = _d01akc));

Error, (in evalf/int) NE_QUAD_MAX_SUBDIV:
  The maximum number of subdivisions has
  been reached: max_num_subint = 500

and

evalf(Int(cos(log(x)/x)/x, x = 0 .. 1, method = _d01akc, methodoptions = [maxintervals = 2000]));

Error, (in evalf/int) NE_QUAD_MAX_SUBDIV:
  The maximum number of subdivisions has
  been reached: max_num_subint = 2000

and

evalf(Int(cos(log(x)/x)/x, x = 0 .. 1, method = _d01ajc));

Error, (in evalf/int) NE_QUAD_NO_CONV:
  The integral is probably divergent or slowly convergent.

Mathematica cracks it without any options, producing 0.323367.

 

------------------------------------------------------------------------------------------------------------------------------

restart:

Digits :=30: m := 4: g :=0.3: nu := 0.4: a := 1:k:=0.2:

W:=cos(n*2*evalf(Pi)*( r-k*a)/((1-k)*a)):

ODE:=((2*(diff(W, r, r, r, r))+2*(diff(W, r, r, r))/r-4*(diff(W, r, r))/r^2+4*(diff(W, r))/r^3-(2*(1-nu))*(diff(W, r, r, r))/r+(4*(1-nu))*(diff(W, r, r))/r^2-(4*(1-nu))*(diff(W, r))/r^3)*r*(1+g*r/a)^3+(2*(2*(diff(W, r, r, r))+2*(diff(W, r, r))/r-2*(diff(W, r))/r^2-(2*(1-nu))*(diff(W, r, r))/r+(2*(1-nu))*(diff(W, r))/r^2))*(1+g*r/a)^3+(6*(2*(diff(W, r, r, r))+2*(diff(W, r, r))/r-2*(diff(W, r))/r^2-(2*(1-nu))*(diff(W, r, r))/r+(2*(1-nu))*(diff(W, r))/r^2))*r*(1+g*r/a)^2*g/a+(6*(2*(diff(W, r, r))+2*(diff(W, r))/r-(2*(1-nu))*(diff(W, r))/r))*(1+g*r/a)^2*g/a+(6*(2*(diff(W, r, r))+2*(diff(W, r))/r-(2*(1-nu))*(diff(W, r))/r))*r*(1+g*r/a)*g^2/a^2-((2*(diff(W, r, r, r)+(diff(W, r, r))/r-(diff(W, r))/r^2))/r-(2*(diff(W, r, r)+(diff(W, r))/r))/r^2-(2*(1-nu))*(diff(W, r, r, r))/r+(2*(1-nu))*(diff(W, r, r))/r^2)*r*(1+g*r/a)^3-((2*(diff(W, r, r)+(diff(W, r))/r))/r-(2*(1-nu))*(diff(W, r, r))/r)*(1+g*r/a)^3-(3*((2*(diff(W, r, r)+(diff(W, r))/r))/r-(2*(1-nu))*(diff(W, r, r))/r))*r*(1+g*r/a)^2*g/a)/(2*(diff(W, r, r))*r+2*(diff(W, r))) :

for i from 1 to m do  for j from 1 to m do
C[i,j]:=int(subs(n=i,ODE)*subs(n=j,W),r=k*a..a)
end do:end do:

why when maple cant solve the following?

  restart: with(plots):
  H := a -> piecewise(a>=0,1):
  f1 := y->(H(y-1*Pi)-H(y-2*Pi))*sin(y)^2:

  g1:=(f1(y)/sqrt(4*Pi*t))*(sin((x-y)^2/4/t+Pi/4)-sin((x+y)^2/4/t+Pi/4)):
  g2:= int(g1, y= 0..100):

  g3:= diff(g2,t):
  g4:= diff(g2,x$2):
  g5:= (g3^2+g4^2)/2:
  E2:= unapply(Int(g5, x= 0..100, epsilon= 1e-4, digits= 7), t):
  CodeTools:-Usage( plot(E2, 0..20, numpoints= 50, labels= [t, E]));

The above mentioned code should give constant figure, but it takes a lot of time and not accurate.

If you can help me to improve these codes, I would be pleased.

 

Thanks!

I need a help about running the following codes..

 

restart:
d:=1:
s:=0.8:
c1:=sqrt((s)/Pi/r^3)/2 * (-sin(r*(u-1)^2/4/(s)+Pi/4)+sin(r*(u+1)^2/4/(s))/sqrt(2)):


c22:=-((u+1)/(4*Pi*r*sqrt(y-1)))*(exp(-r*y*(u+1)^2/(8*s)))*(sin(r*y*(u+1)^2/8/(s*(y-1))+Pi/4)/2+sin(r*y*(u-1)^2/8/(s*(y-1))+Pi/4)):
c2:=Int(c22, y= 1..100):


c33:=(sin(r*y*(u+1)^2/8/(s*(y-1))+Pi/4)+sin(r*y*(u-1)^2/8/(s*(y-1))+Pi/4))*(((d*s)/(Pi*(r^2)*y*sqrt(y-1))*exp(-r*y*(u+1)^2/8/s))-((d^2*sqrt((2*s^3)/(Pi*(y-1)*y^3*r^5)))*exp(d*(u+1)+(2*d^2*s)/(y*r))*erfc((r*y*(u+1)+4*d*s)/(2*sqrt(2*s*r*y))))):
c3:=Int(c33, y= 1..100):


g1:=c1+c2+c3:
g2:= unapply(Int(g1, r= 1..infinity, epsilon=1e-4,digits=7),u):
plot(g2, 0..10, numpoints=100);


 

Thank you!

Dear All

I am trying to integrate a function, however Maple is not giving me the results. I have tried to use int as well as evalf however I am still not getting the results.

 

I would be grateful if you could please suggest me a way out. I have attached the maple file for your reference.

 

ThanksExample.mw

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))

Hello Everyone

I have an expression which I wish to integrate. I would be grateful if you could please help me with it. I have uploaded the maple file for your refrence.

Thanks a lot for your time.

 

 

IntegrationExample.mw

 

Consider

> z := Int(f(t-s), s=0..1);

Int(f(t-s), s = 0 .. 1)

The result is clearly a function of t (and definitely not a function of s, which is a dummy variable).  Let's define

> F := unapply(z, t);

proc (t) options operator, arrow; Int(f(t-s), s = 0 .. 1) end proc

Then

> F(q);

Int(f(q-s), s = 0 .. 1)

as expected.  However:

> F(s);

Int(f(0), s = 0 .. 1)

which is not correct, as this confuses the argument s of F with the dummy integration variable s.  How would you salvage the situation?

 

I am performing the int operation on an experssion but it does not consider constants to be constants. For example, maple is considering this constant namely, f'(-1) or eval(diff(f(x), x), x=-1) as a function and henceforth does not give the desired output. Please tell me how to make eval(diff(f(x), x), x=-1) as a constant function or to say, how to convert any given function in to a constant function.

Thank you for your time and help!

We're starting on indefinite integrals in my 1st year calculus class.

 

A quick example would be int(sin(x), x);=-cos(x)+C

 

Maple doesn't add the +C on the end of it's solution. Can someone explain or point me to a resource? I've tried searching but I can't find an answer. 

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