You are Here: Home >< Maths

1. Can anyone help me explain this?
2. (Original post by SWISH99)

Can anyone help me explain this?
X^-2 is not continuous in the interval [-1,1] and so the integral isn't valid - you'd have to do the integral from -1 to 0 and add it to the integral from 0 to 1 for it to work - of cord rhr winter all doesn't exist as the area is infinite which explains why the answer is not -2.
3. X-2 has a singularity at 0, and cannot be integrated over [-1, 1] in the way shown in the grey box. Indeed, see that for a in (0, 1):

int_{a}^{1} x^-2 dx = -(1)^-1 - (-a)^-1 = (1/a)-1
int_{-1}^{-a} x^-2 dx = -(-a)^-1 - (-(-1)^-1) = (1/a)-1

are both positive as expected. However, neither of those integrals converge at the limit where a goes to 0.
4. As others above this post have stated, f(x) = x^(-2), is not continuous in all of the interval [-1,1] due to the presence of a sigularity at x=0.
Therefore, we can not use the Fundamental Theorem of Calculus.

If we try to apply improper integration:

which does not converge as of course 1/a does not have a limit/converge as "a" goes to 0.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 29, 2017
Today on TSR

### Results day under a month away

How are you feeling?

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams