# Integration of functions of 1 and 2 vaiables

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Ashok Das il 30 Giu 2021
Modificato: Amit Bhowmick il 1 Lug 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?
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### Risposte (1)

Amit Bhowmick il 1 Lug 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)
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Ashok Das il 1 Lug 2021
That's what I am asking for. If we have to use "integral", then we have to make the function in the form
fun = @(x,y) ________
However, in my case the function is of not this form.
Can you give an example for this?
Thank you.
Amit Bhowmick il 1 Lug 2021
Modificato: Amit Bhowmick il 1 Lug 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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