You are Here: Home >< Maths

# Integration query Watch

1. Why is the integral of x^-2 = (1/-1)*x^-1

BUT

(1-x)^-2 = (1-x)^-1 i.e. not (1/-1)*(1-x)^-1

Thanks
2. For the second one, you have to take into account the minus sign in front of the x.

You can check this by differentiating the solution.
3. (Original post by marcusmerehay)
For the second one, you have to take into account the minus sign in front of the x.

You can check this by differentiating the solution.
yeh exactly. you differentiate (1-x)^-1 and you get (x-1)^-2 not (1-x)^-2.

So then why is it when you differentiate (1-x)^-2 you get (1-x)^-1. Shouldnt it be MINUS (1-x)^-1.
4. (Original post by sonic23)
Why is the integral of x^-2 = (1/-1)*x^-1

BUT

(1-x)^-2 = (1-x)^-1 i.e. not (1/-1)*(1-x)^-1

Thanks

You need to consider the coefficient of 'x', which in this case is -1, hence the -1 multiplies with the -1 obtained due to the power to give 1.
5. (Original post by sonic23)
yeh exactly. you differentiate (1-x)^-1 and you get (x-1)^-2 not (1-x)^-2.

So then why is it when you differentiate (1-x)^-2 you get (1-x)^-1. Shouldnt it be MINUS (1-x)^-1.
Differentiating gives
6. (Original post by raheem94)

You need to consider the coefficient of 'x', which in this case is -1, hence the -1 multiplies with the -1 obtained due to the power to give 1.
Thanks
7. (Original post by raheem94)
Differentiating gives
I was using Wolfram.

And just realised (x-1)^-2 = (1-x)^-2

Thanks anyway
8. (Original post by sonic23)
I was using Wolfram.

And just realised (x-1)^-2 = (1-x)^-2

Thanks anyway
THe left therm is reciprocal of and the other
Because both quadratic term is positive and the bases of the powers differ only a minus sign, but
that is

Updated: May 10, 2012
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:
Today on TSR

### Stuck for things to do this summer?

Come and get some inspiration.

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