When to include absolute value sign?

[soccerboi]

When antidiffing, how do you determine if the absolute sign is necessary?

e.g antiff (x+3)/(1+x²), why is it not needed here?

Thanks

[b^3]

Working through the problem.

Now as for all . So that means that the mod will have no affect on it, i.e. making a positive number positive is doing nothing.
So we have

So basically to answer the actual question we can remove the modulus when the thing inside the modulus is always positive (or positive for a given domain if we restrict it).

So to check this, you can either
1) draw it out

2) Look at it logically, will always be positive as we square the number, then adding to it will make it remain positive, so for all .

[TommyLie]

Is it wrong to put a modulus on something which will be >0 anyway? Will you lose marks for it?

[BubbleWrapMan]

Is it wrong to put a modulus on something which will be >0 anyway? Will you lose marks for it?

I wouldn't say so. You should be mindful of it though, I've seen a fair amount of questions that require the removal of the modulus signs to proceed, but in questions like soccerboi's example it shouldn't cost you a mark.

However, if you do remove the signs, it's a good idea to justify it (say something like "as x^2 + 1 > 0").