I have a function which is like f(a,x). I want to numerically integrate it with respect to x, for example using quad function and get factor a in the output. Can someone share how can I achieve this?

I have a function which is like f(a,x). I want to numerically integrate it with respect to x, for example using quad function and get factor a in the output. Can someone share how can I achieve this?

[Walter Roberson]

Is "a" numeric for this purpose, or symbolic? If it is symbolic then you will not usually be able to do numeric integration.

Answer 1

[Mike Hosea]

Having a in the output implies symbolic integration, not numerical. I don't know your use case, but possibly you would find it acceptable to define a function of a like so:

g = @(a)integral(@(x)f(a,x),xmin,xmax)

Then you could evaluate g( a ) for any value of a that you like. If you need it to be vectorized (so that you can evaluate with a vector of a values)

h = @(a)arrayfun(g,a)

can be evaluated at a vector of a values. For example, try this

f = @(a,x)sin(a*x.^2);
g = @(a)integral(@(x)f(a,x),0,pi);
h = @(a)arrayfun(g,a);
a = linspace(0,pi,100);
plot(a,h(a))

If you don't have R2012a or later, you can use QUADGK instead of INTEGRAL. -- Mike