Integration Question: Solutions & Tips

[KingBigness]

Deleted

 

[LeonhardEuler]

The integral of 1/x with respect to x is ln|x| + C, so if you took the integral from a to b, you would get
ln|b|-ln|a|
and as a goes to 0, this would be infinity.

(Note that you shouldn't say you integrate 1/x from 0 to x. You can't have the limit be the variable you are integrating. If you think about what that would mean, you will see that the integral 0f f(x) from 0 to x is impossible to make sense of, since x would vary from 0 to x, whatever that means)

 

[KingBigness]

Yer I did abuse the notation a little, sorry for that.

And sorry for the question as soon as I posted it I realized how stupid it was, hence the delete.

I was just reading a paper on zero and infinity and it got me thinking...the paper didn't really like infinity.

 

[KingBigness]

What I was questioning is, because the curve never reaches the y-axis (x=0), except for at infinity, then the little area between the curve and the y axis, whilst getting smaller and smaller never quite ends.

 

[daveb]

What I was questioning is, because the curve never reaches the y-axis (x=0), except for at infinity, then the little area between the curve and the y axis, whilst getting smaller and smaller never quite ends.

The same could be said for 1/x², but the definite integral does have a value (assuming the lower limit isn't at 0).