Integration of two functions, one of them is piecewise function

Consider the function

p(µ, σ, t, x) = exp(-m*t)/x*sqrt(2*pi*(q.^2)*t)*exp(-1/(2*(q.^2)*t)*(log(x)-(m-(q.^2)/2)*t).^2)  (0 < x < ∞)

Here let µ = .02, σ = .18 and t = .25, so p is a function on the variable x only. I created a function file pfun.m for this function, having µ, σ, t and x as input.

I need to compute int(C(x)*p(x),x,0,inf)

where C(x) = 0 if x < 1.02

x − 1.02 otherwise

Answer 1

[Walter Roberson]

general_p = @(m, q, t, x) exp(-m.*t) ./ x .*sqrt(2*pi*(q.^2).*t) .* exp(-1/(2*(q.^2).*t) .* (log(x)-(m-(q.^2)/2) .*t ).^2);
p = @(x) general_p(0.02, 0.18, 0.25, x);
C = @(x) (x - 1.02) .* (1.02 <= x);
result = integral(@(x) C(x) .* p(x), 0, inf)

[Hanson Zhou]

Hi Walter,

Thanks for sharing. When I run these codes, it gives me en error:

Error using sym/subsindex (line 663) Invalid indexing or function definition. When defining a function, ensure that the body of the function is a SYM object. When indexing, the input must be numeric, logical or ':'.

Do you know how to solve it?

[Walter Roberson]

I have adjusted the code, above.

[Hanson Zhou]

Thank you so much. Sry about the late replay