# Integration of functions of 1 and 2 vaiables

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Ashok Das on 30 Jun 2021
Edited: Amit Bhowmick on 1 Jul 2021
I have two questions:
1. I have a function like this: f(x) = 1 (if x=0) and f(x)=0 (if x~=0). How can I integrate between any interval (a,b)?
2. Two-dimensional function: f(x,y) is given. How can I integrate f(x,y) with respect to only the variable 'x', while keeping 'y' fixed?

Amit Bhowmick on 1 Jul 2021
1. You can use dirac function to define,
syms x
f=dirac(x)
intf=int(f,x) %Indefinite integration
intfd=int(f,x,[a b] %definite integration
2. For question 2 use this
syms x y
f=x^2+y^3
intf=int(f,x)
Amit Bhowmick on 1 Jul 2021
Edited: Amit Bhowmick on 1 Jul 2021
If you keep y fixed then it would be symbol only unless you provide some value of y. I think integral function does pure numerical integration (You can check reference page). hence it is not possible to integrate using integral where y is a symbol. So you can do one thing make an array of Y=a:b,
and put y=Y(ii) and then integrate using integral(f,ax,bx) where f=@(x) ax+by+c (say)
or use integral2(f,ax,bx,ay,by) f=@(x,y) ax+by+c

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