Numerical integration of a long symbolic expression with definite limits

I want to numerically integrate a long symbolic expression with definite limits without using the symbolic integration function (int) because it is very slow. A sample example (for short expression) would be

syms t a b c 
y=a*sin(t)+(b*cos(2*t)+c*sin(3*t))^2

I want to integrate y with respect to t from 0 to pi. The result should be a symbolic expression in a , b, c.

Again, I don't want to use int function

[Torsten]

If you don't want to assign numerical values to a,b and c, the only choice you have in Matlab is the 'int' function.

Or you use

syms a b c

Y= a*integral(@(x) sin(x),0,pi)+b^2*integral(@(x)cos(2*x),0,pi)+c^2*integral@(x)sin(3*x),0,pi)+ ...

2*b^2*c^2*integral(@(x)cos(2*x).*sin(3*x),0,pi)

[Mohammed]

Thank you for your answer and effort. However, this does not work for long expression

[Torsten]

Why ?

[Walter Roberson]

There are some thing you can do with children() and symType() and symFunType() to figure out which parts you can do numerically.

However... you would probably find that vpa() of the expression before doing int() would have the same effect.

[Mohammed]

Why?

Assume we have

y=(a*sin(t)+a*sin(5*t)+(b*cos(2*t)+c*sin(3*t))^2)^10

No way to collect the cofficites of the trignometric functions

[Walter Roberson]

?

The result of int(y) would not have any trignometric expressios left in it, just combinations of a, b, c, pi, and fractions. a appears up to a^10, b appears up to b^20, c appears up to c^20. You can extract the coefficients using coeff()

You can expand() y and work term by term, using children(), extract the symbolic coefficient multipliers, do numeric integration on the sin()^n*cos()^m part, multiply by the symbolic parts, record, and later sum() all the results. It is not clear this would be any more useful than using int(y) or int(vpa(expand(y)))

[Mohammed]

I am responding to Torsten question