# Question:How to integrate the computed values

## Question:How to integrate the computed values

Maple 18

Dear maple users,

A fine day wishes to all.

Here, we have computed the fN(x,t) value by using pdsolve.

We have to integrate the computed value and need to find the values with the sequence of x.

A1:=int(fN(x,1.12),x)

A2:=seq(A1,x=0..1,0.1)

How to integrate the computed values

And, How to find the values for the sequence of x.

 > restart:
 > with(PDEtools):
 > with(plots):
 > fcns := {f(x,t)};
 (1)
 > b1:=1.41:d:=0.5/1:xi:=0.1:ea:=0.5:ra:=2:
 > L:=z->piecewise(d<=z and z<=d+1, 1-2*xi*(cos((2*3.14)*((z-d)*(1/2))-1/4)-(7/100)*cos((32*3.14)*(z-d-1/2))),1):
 > PDE1 :=ra*(diff(f(x,t),t))=+b1*(1+ea*cos(t))+(1/(L(z)^2))*((diff(f(x,t),x,x))+(1/x)*diff(f(x,t),x));
 (2)
 > IBC := {D[1](f)(0,t)=0,f(1,t)=0,f(x,0)=0};
 (3)
 > z:=0.5;
 (4)
 >
 > sol:=pdsolve(eval([PDE1]),IBC ,numeric, time = t,spacestep = 0.025, timestep=0.0001): sol:-value(f(x,t), output=listprocedure);
 (5)
 > fN:=eval( f(x,t), sol:-value(f(x,t), output=listprocedure)):
 >
 > A1:= int(fN(x,t),x);
 (6)
 > A2 := seq(A1(x), x = 0.1 .. 1, 0.1);
 >