How to use integral when limits are anonymous functions

Greetings

I am evaluating an integral wherein the limits are functions themselves and symbolic variables are involved. I can't use int because it does not yield a complete answer (some of the integrals couldn't be solved symbollically), hence I am using integral with ArrayValued enabled.

My code is something like this:

syms x y(x) f(x,y)
dx = 1e-8;
I = @(x) integral( @y f(x,y), y1(x), y2(x), 'ArrayValued', true)
dI = (I(x=x_0+dx) - I(x))/dx + other leibniz terms as limits are functions of x

When I run this code, I get that A and B ( the limits in the integral function must be floating point scalars)

How do I overcome this?

Answer 1

[Walter Roberson]

Your problem is unsolvable (in the form stated)

You cannot use integral() with symbolic limits: integral() is strictly a numeric integrator, and cannot handle symbolic limits.

You need to use int(), and just live with the fact that int() is unable to find a solution.

[Aviral Srivastava]

It is actualy a combination of anonymous function of symbolic variables.

syms x y(x)

correction: f = @(x,y) f(x,y)

dx = 1e-8;

I = @(x) integral( @y f(x,y), y1(x), y2(x), 'ArrayValued', true)

dI = (I(x=x_0+dx) - I(x))/dx + other leibniz terms as limits are functions of x

Earlier my code was working fine when I assigned the limits for a particular x. However, as a part of my research I intend to study the variation with both x and y and am encountering the problem mentioned above.

What solution I tried: I converted the symbolic limits to anonymous function through the matlabFunction() but still encountering the same error.

[Walter Roberson]

I = @(x) integral( @y f(x,y), y1(x), y2(x), 'ArrayValued', true)

is not valid syntax. Perhaps you meant

I = @(x) integral( @(y) f(x,y), y1(x), y2(x), 'ArrayValued', true)

[Walter Roberson]

integral() does not support functions for its limits.

For any one numeric x, you can calculate y1(x), y2(x) and use those constants in integral(). However, you cannot do this for generic symbolic x.