# Question:unevaluated integral

## Question:unevaluated integral

Maple

[Preliminary analysis of the Question by Carl Love:

In the worksheet below, the OP numerically solves a BVP on an interval a..b, for several values of a parameter. Using the numeric solution procedures returned by dsolve, he wants to numerically integrate an algebraic expression (named P1 below) that uses several of the BVP's dependent variables as well as its independent variable. This integral is to be done on an interval c..d, where a < c < d < b (all inequalities strict). He's having trouble coming up with the correct syntax for this.

I (Carl) am confident that the dsolve calls are all syntactically correct and that they return solution procedures in the usual manner without raising any issues, numerical or otherwise. Whether the integrations will ultimately require some adjustments to dsolve's error-control options, I don't know at this point. This Question is only about syntax required to perform the integrations. Any error-control adjustments, if they're needed at all, will be handled later.

I (Carl) have only edited the the OP's worksheet to remove a large amount of content that is irrelevant to Answering this Question. I haven't changed any of the content; I've only deleted. Of course, I already have several ideas about what needs to be done, but up until this point I haven't acted as an Answerer but rather as a Moderator and Editor making this Question suitable for posting.

--Carl Love]

 > restart;
 >
 > 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:
 > de:=eq1,eq2,bcs:
 > d1 := subs(Uhs =-2, zeta=3,k=1,[de]):
 > param:= {Uhs =-2, zeta=3,k=1}:
 > P1:= eval(diff(f(y), y\$3)+Uhs*diff(E(y),y\$2)-(diff(f(y), y\$1)+1)+(theta(y))+sin(alpha),param);
 (1)
 > ec:=0.5:
 >
 > for Q from -3 to 3 by ec do F2[Q]:=dsolve(d1, numeric,maxmesh=25500,continuation=lambda1,output=listprocedure): P2[Q]:=subs(F2[Q],P1):   end do:
 > for Q from -3 to 3 by ec do P3[Q]:=evalf(Int(P2[Q],0..1));    end do:

[Examination of any of the P2[Q] or P3[Q] will highlight the syntactic problem. --Carl]:

 > P2[-3];
 (2)
 > P3[-3];
 (3)
 >

Note: If I remove the cosh from P1 then everything works fine.