# Oxford PAT 2011, Question 8

## 5 thoughts on “Oxford PAT 2011, Question 8”

1. sam says:

what method of integration is this?

2. Hi, thanks for the comments. You are absolutely right, both answers have silly mistakes in them.

In part (i) the answer correctly derives the simultaneous equations a + b = 1 and -a + b = 2, but the solution to these should be b = 3/2 and a = -1/2, and this makes your final answer correct.

In part (ii) there is an attempt to use the substitution u = x + 1, but the substitution doesn’t actually get made. If you do the substitution properly, the integral becomes Integral from 1 to 2 of (1 / sqrt(x)) dx. This gives us 2 sqrt(2) – 2 sqrt(1), which is 2(sqrt(2) – 1), as you say in your comment.

Thanks very much for your corrections; it’s so easy for careless errors to creep in to these answers and it’s really useful to get contributions from people who spot them.

1. Rickardo says:

could the first answer be represented as 1/2(In|(x-1)^3/(x+1)|)+c?
Hope you can clarify this for me please. And if its correct is it fine to leave the c outside because physicsmathstutor has this solution which confused me a little: http://www.physicsandmathstutor.com/pat/solutions-2011/

Thank you!

1. Yes it is fine to leave the c outside. Remember that ln(x) + ln(y) = ln(xy), so ln(x) + c = ln(Ax) where ln(A) = c. So you could rewrite my answer as ln(A(x-1)^3/(x+1))/2. This is the same form as the answer you refer to in the link.