Error using Integral - IntegralCalc - Syms

Hi, This is my Code

clc
clear all
syms Th
th1=5*pi/12 ; 
th2=7*pi/12;
A11= @(Th) (10279222485063723*cos(Th).^2)/2684354560000 + (9*((7138348947960919*cos(Th).^2)/8589934592 + 1142135831673747/4294967296))/(625*cos(Th).^2) 
A11Bar=integral(A11,th1,th2)
Acap =(10279222485063723*cos(Th).^2)/2684354560000 + (9*((7138348947960919*cos(Th).^2)/8589934592 + 1142135831673747/4294967296))/(625*cos(Th).^2) 
Acap11 =  @(Th) Acap
Acap11Bar=integral(Acap11,th1,th2)

I am trying to Integrate the Equation in A11 with limits th1 and th2. Using the Integral command, If I am using the equation directly it gives me the answer. But if Define the equation as Acap, Acap becomes symbolic and I dont get answer and the error comes as follows. My Question is , Th is a sym, but I get the answer for A11Bar, when using Th in A11, But why not the same in the other case.

A11 =

    @(Th)(10279222485063723*cos(Th).^2)/2684354560000+(9*((7138348947960919*cos(Th).^2)/8589934592+1142135831673747/4294967296))/(625*cos(Th).^2)

A11Bar =

     4.090565444758960e+04

Acap =

(2569805621265931*cos(Th)^2)/671088640000 + ((64245140531648271*cos(Th)^2)/8589934592 + 10279222485063723/4294967296)/(625*cos(Th)^2)

Acap11 =

    @(Th)Acap

Error using integralCalc/finalInputChecks (line 511) Input function must return 'double' or 'single' values. Found 'sym'.

Error in integralCalc/iterateScalarValued (line 315) finalInputChecks(x,fx);

Error in integralCalc/vadapt (line 132) [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75) [q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral (line 88) Q = integralCalc(fun,a,b,opstruct);

Error in Untitled (line 13) Acap11Bar=integral(Acap11,th1,th2)

Answer 1

[Torsten]

Use

Acap11 = matlabFunction(Acap)

Best wishes

Torsten.

[Muthu Ram Prabhu Elenchezhian]

Hi Torsten, Thanks for your response, it did work, but there are few errors. Could you help on it as the answer varies.

A11 =

function_handle with value:

    @(Th)(10279222485063723*cos(Th).^2)/2684354560000+(9*((7138348947960919*cos(Th).^2)/8589934592+1142135831673747/4294967296))/(625*cos(Th).^2)

A11Bar =

   4.0906e+04

Acap =

(2569805621265931*cos(Th)^2)/671088640000 + ((64245140531648271*cos(Th)^2)/8589934592 + 10279222485063723/4294967296)/(625*cos(Th)^2)

Acap11 =

function_handle with value:

    @(Th)cos(Th).^2.*3.829308779933946e3+1.0./cos(Th).^2.*(cos(Th).^2.*7.479118710808487e6+2.393317987458716e6).*(1.0./6.25e2)

Warning: Minimum step size reached near x = 1.5708. There may be a singularity, or the tolerances may be too tight for this problem. > In integralCalc/checkSpacing (line 456) In integralCalc/iterateScalarValued (line 319) In integralCalc/vadapt (line 132) In integralCalc (line 75) In integral (line 88) In Untitled (line 12)

Acap11Bar =

   1.9726e+17

[Torsten]

cos(Th) = 0 at Th=pi/2, so you divide by 0.

Best wishes

Torsten.

[Muthu Ram Prabhu Elenchezhian]

Hi Torsten,

But if you check in my program given above, I have set the limits from 75 degrees to 105 degrees. I have not used 90 degrees ( pi/2 ) .

clc
clear all
syms Th
th1=5*pi/12 ; 
th2=7*pi/12;
A11= @(Th) (10279222485063723*cos(Th).^2)/2684354560000 + (9*((7138348947960919*cos(Th).^2)/8589934592 + 1142135831673747/4294967296))/(625*cos(Th).^2)

A11Bar=integral(A11,th1,th2)

Acap =(10279222485063723*cos(Th).^2)/2684354560000 + (9*((7138348947960919*cos(Th).^2)/8589934592 + 1142135831673747/4294967296))/(625*cos(Th).^2) Acap11 = matlabFunction(Acap) Acap11BarA=integral(Acap11,th1,th2)

A11 =

function_handle with value:

    @(Th)(10279222485063723*cos(Th).^2)/2684354560000+(9*((7138348947960919*cos(Th).^2)/8589934592+1142135831673747/4294967296))/(625*cos(Th).^2)

A11Bar =

   4.6631e+04

Acap =

(2569805621265931*cos(Th)^2)/671088640000 + ((64245140531648271*cos(Th)^2)/8589934592 + 10279222485063723/4294967296)/(625*cos(Th)^2)

Acap11 =

function_handle with value:

    @(Th)cos(Th).^2.*3.829308779933946e3+1.0./cos(Th).^2.*(cos(Th).^2.*7.479118710808487e6+2.393317987458716e6).*(1.0./6.25e2)

Warning: Minimum step size reached near x = 1.5708. There may be a singularity, or the tolerances may be too tight for this problem. > In integralCalc/checkSpacing (line 456) In integralCalc/iterateScalarValued (line 319) In integralCalc/vadapt (line 132) In integralCalc (line 75) In integral (line 88) In Untitled (line 12)

Acap11BarA =

   1.1694e+18

[Torsten]

90° is in between 75° and 105°, and you integrate over the entire interval.

Note that x=1.5708 is approximately pi/2.

Best wishes

Torsten.

[Muthu Ram Prabhu Elenchezhian]

Hi, Thanks. I understood it now