Question
Evaluate the definite integral $\int\limits_2^3 {\frac{{dx}}{{{x^2} - 1}}} $
$= \left( {\frac{1}{{2\left( 1 \right)}}\log \left| {\frac{{x - 1}}{{x + 1}}} \right|} \right)_2^3$
$= \frac{1}{2}\log \left| {\frac{{3 - 1}}{{3 + 1}}} \right| - \frac{1}{2}\log \left| {\frac{{2 - 1}}{{2 + 1}}} \right|$
$= \frac{1}{2}\log \left| {\frac{1}{2}} \right| - \frac{1}{2}\log \left| {\frac{1}{3}} \right|$
$= \frac{1}{2}\left( {\log \frac{1}{2} - \log \frac{1}{3}} \right)$
$= \frac{1}{2}\log \frac{{\frac{1}{2}}}{{\frac{1}{3}}}$
$ = \frac{1}{2}\log \frac{3}{2}$
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The number of contacts of each type made in two cities X and Y is given in matrix B as
$\text{BA}=\begin{bmatrix}\text{Telephone}&\text{House call}&\text{Letter}\\1000&500&5000\\3000&1000&10000\end{bmatrix} \begin{matrix}\rightarrow\text{X}\\\rightarrow\text{Y}\end{matrix}$
Find the total amount spent by the group in the two cities X and Y.