You are Here: Home >< Maths

# STEP Question watch

1. I did this one in the exam:

use the substitution x=sec(t) to show that

(integral between upper:2 and lower:root 2) 1/(x^3*root(x^2 - 1)) dx = (root(3) - 2)/8 + (pi)/24

I get

1/8 - (pi)/24

Anyone see how to do it? (Sorry about the notation - I hope they enable LaTeX here some time!)

Thanks
2. (Original post by sat)
I did this one in the exam:

use the substitution x=sec(t) to show that

(integral between upper:2 and lower:root 2) 1/(x^3*root(x^2 - 1)) dx = (root(3) - 2)/8 + (pi)/24

I get

1/8 - (pi)/24

Anyone see how to do it? (Sorry about the notation - I hope they enable LaTeX here some time!)

Thanks
I get the answer, the integral should simplify to cos^2(t) with bounds as pi/3 and pi/4.
3. (Original post by sat)
I did this one in the exam:

use the substitution x=sec(t) to show that

(integral between upper:2 and lower:root 2) 1/(x^3*root(x^2 - 1)) dx = (root(3) - 2)/8 + (pi)/24

I get

1/8 - (pi)/24

Anyone see how to do it? (Sorry about the notation - I hope they enable LaTeX here some time!)

Thanks
x = sect , so dx = [sint/(cost)^2] dt
x : sqrt(2) -> 2, so t : pi/4 -> pi/3
x^3sqrt(x^2 - 1) = (sect)^3.tant = sint/(cost)^4
I = integration { (cost)^4/sint * sint/(cost)^2 dt }
= I{(cost)^2dt}
= 1/2* I{cos2t - 1)dt}
= 1/2* (sin2t/2 - t) (pi/4 -> pi/3)
= 1/4*[sin(2pi/3) - sin(pi/2)] - pi/24
= (sqrt(3) - 2)/8 - pi/24.
4. I had got down to the cos^2 bit previously, but I must have chosen the wrong set of trig. identities to go fro there. I did get there in the end!
5. I remember doing that question, is it from this year's paper?

### 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: August 7, 2004
Today on TSR

### Edexcel GCSE Maths Unofficial Markscheme

Find out how you've done here

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