Can I use integral with symbolic/variable interval values?

Hi. I'm wondering if it is possible to use, in some way, variable or symbolic interval values for the integral function. I need to solve a similar kind of problem shown below, can't think of a way to do it (my functions are quite huge, so it's not easy to somehow simplify it).

• Function 1: f(s)=...
• Function 2: g(x)=...
• f_new = integral(@(s) f, 0, x)

Now, both f_new and g is a function of x.

• Final function = integral(@(x) f_new*g, 0, 2)

Hope the question is somewhat clear. If not, just ask. Any help is appreciated! :)

Answer 1

[Walter Roberson]

Assuming that f is a function handle already, such as

f = @(s) tan(s^2 + exp(-s));

then

f_new = @(x) integral(f, 0, x);
final_function = @(b) integral( @(x) f_new(x) .* g(x), 0, b);

and

final_function(2)

[Mike Hosea]

You will need to vectorize f_new with arrayfun, e.g.

f_new = @(v)arrayfun(@(x)integral(f,0,x),v)

or, alternatively, prevent the outer integral from passing in non-scalars with the 'ArrayValued' option:

final_function = @(b)integral(@(x)f_new(x).*g(x), 0, b,'ArrayValued',true);

[giorgio vanni]

I've copied the answer from Walter in an easier version, as follows:

fun=@(y)integral(@(x)x,0,y)

integral(fun,0,1)

But what I've obtained is the following:

Error using integral (line 85)

A and B must be floating-point scalars.

Error in @(y)integral(@(x)x,0,y)

Error in integralCalc/iterateScalarValued (line 314)

fx = FUN(t);

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);

I can't understand where is the problem, can you help me?

Answer 2

[Brede Løvik Lillehammer]

Thanks for your help guys! This works. Also found the function int(), which seems to do the same thing if I'm not mistaken.

[Walter Roberson]

int() is for symbolic integration. integral() is for numeric integration.