# Integration numerical with variable limits

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DM on 3 Oct 2014
Commented: Vivek Sharma on 16 Jun 2021
I am trying to find a double integration numerically where the inner integral has variable limits while the outer integral has scalar limits and not the other way round. As I understand integral2 allows you do the reverse of what I want i.e you can have the outer variable limits non scalar while the inner should be scalar.
fxy=@(x,y)1/x+1/y
xmin=0;
xmax=@(y)2*y;
ymin=0;
ymax=+inf;
integral2(fxy,xmin,xmax,ymin,ymax)
I get the following error
Error using integral2 (line 76)
XMAX must be a floating point scalar.

Mike Hosea on 3 Oct 2014
The INTEGRAL2 interface is set up to calculate an iterated integral where the integral over the second argument of the integrand function f is the inner integral. It does not matter what you call your variables, whether it be x, y, t, p, r, or whatever. The first argument is the outer integral, and the second argument is the inner integral. If your problem happens to be formulated so that the inner integral variable is called x and the outer integral variable is called y, but your integrand is already defined so that x is the first argument and y is the second, then you just do this:
integral2(@(y,x)f(x,y),ymin,ymax,xmin,xmax)
Your example isn't integrable, or I'd demonstrate.
Vivek Sharma on 16 Jun 2021
This comment was flagged by Steven Lord
Dear Sir,
Hope you are fit and sailing the storm perfectly.
I need help in writing a MATLAB code for the problem attached herewith .
I shall be thankful to you.
Best Wishes,
Vivek Sharma

Alberto on 3 Oct 2014
Edited: Alberto on 3 Oct 2014
There is a general solution using symbolic tools.
syms x y
fxy=1./x+1./y;
xmin=0;
xmax=2*y;
ymin=0;
ymax=+inf
int(fxy,x,xmin, xmax) % integration dx
int(int(fxy,x,xmin, xmax),y,ymin,ymax) % double integration

Andrei Bobrov on 3 Oct 2014
out = integral2(fxy,ymin,ymax,xmin,xmax);
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DM on 3 Oct 2014
What you suggested is performing double integral over dxdy but with the wrong limits since you reversed them @andrei bobrov