Integration of functions of 1 and 2 vaiables

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?

Answer 1

[Amit Bhowmick]

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)

[Ashok Das]

Thanks for your response. Can we do it without using syms function. The functions are not of simple form, sometimes they are given for different conditions (just like question 1).

[Amit Bhowmick]

you can use integral(f,xmin,ymin) but the value of y should be a numerical value not a symbol.

[Ashok Das]

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]

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