numerical integraion with array limits

I am trying to work out the integrals that are function of one of the limits, and both limits are vectors:

n=1:10;

t=2;

a=(n-1).*t;

b=n.*t;

Q=integral(@(x)lognpdf(b-x,2,1),a,b,'ArrayValued',true);

As a and b must be scalars, so integral won’t work here. Someone suggested using arrayfun in the answers to a similar question in April where only one limit is a vector, how to do this?

Answer 1

[Mike Hosea]

Assuming you want each individual integral to be

integral(@(x)lognpdf(b(j)-x,2,1),a(j),b(j))

then

Qab = @(aj,bj)integral(@(x)lognpdf(bj-x,2,1),aj,bj)
Q = arrayfun(Qab,a,b)

You don't have to rename a and b in Qab, as they are "scoped" to be distinct from the previously defined a and b vectors, but I just did it for clarity.

[Wenjuan]

Thanks. Just managed to work this out myself as well.

[Mike Hosea]

Then we'll have you teaching arrayfun usage on MATLAB Central in no time. :)

[Wenjuan]

Now I am trying to work out double integral, where the limit of y is a function of x, like

fun=@(x,y)lognpdf(b-x,2,1).*lognpdf(y,3,2);  
ymax=@(x) b-x;  
Qab=@(a,b)integral2(fun,a,b,0,ymax);  
Q=arrayfun(Qab,a,b);

but this returns error

"

Error using  - 
      Matrix dimensions must agree.
      Error in @(x)b-x"

Is this because b is a vector?

[Mike Hosea]

Yes, but the problem is that the value for b is obtained as a snapshot when @(x)b-x is created. You should be able to work around this problem by inlining the creating of ymax, i.e.

ab=@(a,b)integral2(fun,a,b,0,@(x)b-x);

Answer 2

[Sergio Quesada]

Hi everybody, I'm working on a similar easier case, but with no success... I'm trying to evaluate

liminf=ones(1,20); syms x; 
integral(@(x)exp(-a./x.*log(x)),liminf,r)

beeing 'a' an escalar, and 'r' also a 1x20 array. That is, 20 different integrals from 1 to each value of 'r'

It sais:

 Error using integral (line 85)
A and B must be floating-point scalars.

Thankyou so much !!