Show that: (I don't have any way of showing it properly so have written it in words)
'The integral from 5 to 3 of (sq root (x^2 - 9) ) with respect to x' = 10 - (9/2) * ln 3
I hope that makes sense!
Well I'm not sure.. I *think* that the fact the integral of 1/(sq root (x^2 - a^2)) is arcosh (x/a) is relevant.
The Attempt at a Solution
This is part of the 'hyperbolic functions' section on my exam; so the first thing I know is that they will come into it somehow. I cannot solve this by inspection, or by simply comparing it to all the formulae on my sheet.. I also tried to solve by parts (using difference of two squares to give me a root multiplied by another root) but found that this still gave me something I do not know how to integrate. I know if it was 1/(sq root (x^2 - 9)) it would be easy; but cannot work out how the integral of a particular thing and the integral of 1/it are related.
Thanks in advance.