# Another: dirac_delta integration: possible bug?

I think there is another problem with the integration of the dirac_delta in Sage:

(previous problem is discussed in the thread Integration of dirac_delta)

Here is the problem:

```
var('a',"real")
f=integral(dirac_delta(a*x),x,-oo,oo);show(f)
```

returns `1`

where it should return `1/|a|`

and

```
var('a',"real")
f=integral(dirac_delta(x^2-a^2),x,-oo,oo);show(f)
```

returns `1/|a|`

, where it should be `1/(2|a|)`

I agree with the

`1/|a|`

in the second case, both roots contribute for`1/|2a|`

. Also you may have noticed that the answer I gave you in your other post produces the right answer in the first case, but 0 in the second one. That's because`a<+oo`

is always`False`

. For it to work you have to put assumptions on`a`

, and also not use infinity as a bound.I looked at the code and tried to fix it to accomodate this problem but I wasn't very successful (though I learned a lot!) I tried the following with your version, but I am getting

`0`

.am I using it wrong? (especially the assumptions?)

For me it works with

`x^2-a^2`

instead of`x^2-a`

. If you don't take the square, you need to assume`a>0`

, otherwise there is no real root, the the answer is zero.