## 5408 Reputation

17 years, 226 days
Munich, Germany

## hm ......

@Carl Love What is called "Quantile" seems to be a cumulative for the pdf.

off topic: I dislike questions without giving a context or reference, here it can not be judged (for me) whether it makes sense to treat it with Maple

## will try...

@acer , thank you - I will try that (various versions and also old sheets)

## Re: computational time...

roughly 1 second to compute the anti-derivative

NB: you need "Re( ... )" for plotting because 2F1 may have spurious numerical imaginaries - or use plot( [Re(...), Im(...)], ...)

NB2: do *not* use brackets like " [ ", use ordinary brackets like " ( " in your functions

## correct by + 800*t...

You are right, I made an error through copy + paste and will correct my answer, I have to add 800*t

## test...

Fails for me too (FF 83 portable, I have blocked some servers through DNS, but never observed a problem usinf Mapleprimes)

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/prove.mw .

https://www.mapleprimes.com/questions/231147-Unevaluated-Integral

 > restart; Digits:=10;
 (1)
 > eq1:=diff(f(y), y\$4)+Uhs*diff(E(y),y\$3)-(diff(f(y), y\$2))+(diff(theta(y), y\$1))= 0:
 > eq2:=diff(theta(y), y\$2)+(diff(f(y), y\$2)+1)^2+1+diff(theta(y),y\$2) = 0:
 > E:=y->zeta*(cosh(k/2*(h1+h2-2*y)))/(cosh(k/2*(h1-h2))):
 > bcs:= f(h1) = -(1/2)*(Q-1-d),         f(h2) = (1/2)*(Q-1-d),         (D(f))(h1) = -1,         (D(f))(h2) = -1,         theta(h1) = 0,         theta(h2) = 1:
 > epsilon1:=0.1:                    d:=1:                             omega:=Pi/6:   h1:=-(1+epsilon1*sin(2*Pi*x)):    h2:=d+epsilon2*sin(2*Pi*x+omega): F:= Q-1-d:   epsilon2:=0.5:                    x:=1:                             alpha:=Pi/6:
 > d1 := subs( Uhs =-2,               zeta=3,               k=1,               [eq1, eq2, bcs ]             ):
 > d1_var:=eval(d1, [f=ff, Q=QQ]);
 (2)
 >
 > F:=proc(Q) local deq,sol,g; deq:=eval(d1_var, QQ=Q); sol:= dsolve(deq, numeric, output=listprocedure): g:= unapply( rhs(sol[5])(z)-3.524364340*cosh(-0.1250000000 + rhs(sol[1])(z))-rhs(sol[3])(z)-1/2+rhs(sol[6])(z),z); evalf(Int(g, 0..1, epsilon=1e-8)); end proc:
 > #F(0); # test
 (3)
 > plot(F, -3 .. 3, numpoints=10);
 >

## for the complex case...

Clearly it is never 0. But it can take any other value for x being a complex number: for that write g(x) = 1/w, any w not 0. Then you have cubic in x = w and you know it always has a solution.

## combine         &nbs...

combine                            ?

## plot...

Plot the function - then you see what to do

## Heaviside...

and if not: it should be easy to define such a function (if - else and how to behave at the jump)

## look up the help...

look up the help and find a sheet attached

MP_230629.mws

## remark...

Besides that I doubt you can still buy it:

Version 9.5 is dated, 15 years old. Once I tested it to use it on Windows 7 (~ 2010) and it did not work properly for that operating system.

## experiment...

No typo, it reminds me that I modified the original, https://svn.r-project.org/R/trunk/src/library/stats/src/zeroin.c

## noise...

@vv so you say the random number is added for each call of f ... hm. But the optimum is searched for the (guessed) f0 ? Then I got it wrong

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