## Numerical integration with array limits

### Christopher Kodama (view profile)

on 29 Apr 2013
Latest activity Commented on by Ashish Bhatt

on 10 Apr 2017

### Shashank Prasanna (view profile)

I'm trying to work with integrals that are functions of one of their limits:

For example,

```phi = @(x) quad(@(L) besseli(1, (1+L)/(1-L)), 0, x);
```

What I'm trying to do is evaluate phi over an array of values, like:

```phi([1,2,3,4]); %ERROR
quad(@(L) besseli(1, (1+L)/(1-L)), 0, [1,2,3,4]); %ERROR
```

but these return errors. I could do this in a for loop, like:

```nums=[1,2,3,4];
for(k=1:4)
phi_eval = phi(nums(k));
end
```

but I was wondering if there was a better way to do things. Is there a no-for-loops way of doing this?

### Shashank Prasanna (view profile)

on 29 Apr 2013

Christopher, I can't run the loop as well. But phi([1,2,3,4]) will certainly not work because the vector is being passed to quad directly as limits which is wrong syntax for quad.

You can try the following:

```arrayfun(phi,[1,2,3,4])
```

http://www.mathworks.com/help/matlab/ref/arrayfun.html

Leo Simon

### Leo Simon (view profile)

on 11 Feb 2014

I too would like to specify vector valued integration limits. If anybody from mathworks is listening could you please respond? This should be really easy to implement I imagine, and hopefully will be in the next release?

Mike Hosea

### Mike Hosea (view profile)

on 10 Mar 2014

Please go to my profile. Where it says "email", click on "contact Mike Hosea" and tell me about your use cases for array-valued limits. If we're talking generic array limits, where there is no a priori relationship between the different elements of the limits, then no gain in efficiency can be had over writing a loop. E.g.

```Q = zeros(size(a));
for k = 1:numel(Q)
Q(k) = integral(f,a(k),b(k));
end
```

For scalar-valued integrations, that can also be accomplished efficiently with an application of arrayfun, e.g.

```Qarray = @(a,b)arrayfun(@(ak,bk)integral(f,ak,bk),a,b);
Q = Qarray(a,b);
```

However, if we are talking about table-building, where the limits represent a grid, then efficiency improvements are possible. The latter use case might be accomplished by some other means, however, such as providing scalar limits and a list of output points for the integrals over partial regions.

Ashish Bhatt

### Ashish Bhatt (view profile)

on 10 Apr 2017

it works with both array limits as well:

```phi = matlabFunction(int(x^2,x,a,b));
arrayfun(phi,vec1,vec2)
```

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