integration using two variables

I have two expressions for variables a and x

M = (-150 + 20.556*x - ((1/2)*(x-10)^2 - (1/60)*(x-10)^3))*heaviside(20-x) + (5.556*x+(250/3))*heaviside(x-20);

m = (a*(1-x/30))*heaviside(20-a) + (x*(1-a/30)*heaviside(20-x) + a*(1-x/30)*heaviside(x-20))*heaviside(a-20);

And another expression

Mm = M*m;

I want to integrate Mm with respect to x treating a as a constant from x = 0 to x = 30. How can i do it?

Answer 1

[Walter Roberson]

Use the symbolic toolbox

syms x a
M = (-150 + 20.556*x - ((1/2)*(x-10)^2 - (1/60)*(x-10)^3))*heaviside(20-x) + (5.556*x+(250/3))*heaviside(x-20);
m = (a*(1-x/30))*heaviside(20-a) + (x*(1-a/30)*heaviside(20-x) + a*(1-x/30)*heaviside(x-20))*heaviside(a-20);
Mm = M*m;

result = simplify( int(expand(Mm), x, 0, 30) );