Hi folks,

I am trying to calculate the area between the curve $y = 1 / (x -1)(x - 3) $ and the line $y = - \frac{4}{3} $

The curve cuts the line at A (3/2, -4/3) and B(5/2, -4/3) and we can see the area in the attachment

So, Area, $A = \int_{\frac{3}{2}}^ {\frac{5}{2}} \frac{1}{(x - 1)(x - 3)} $

using partial fractions $\frac{1}{(x - 1)(x - 3)} = \frac{1}{(2x - 6)} - \frac{1}{(2x - 2)} $

so $A = \int_{\frac{3}{2}}^ {\frac{5}{2}} \frac{1}{(2x - 6)} dx - \int_{\frac{3}{2}}^ {\frac{5}{2}} \frac{1}{(2x - 2)} dx$

$A = \frac{1}{2} \int_{\frac{3}{2}}^ {\frac{5}{2}} \frac{2}{(2x - 6)} dx - \frac{1}{2} \int_{\frac{3}{2}}^ {\frac{5}{2}} \frac{2}{(2x - 2)} dx $

$A = \frac{1}{2} \ln | (2x - 6) | - \frac{1}{2} \ln | (2x - 2) | $

$A = [ \ln \frac {\sqrt{| 2x - 6 |}}{\sqrt{| 2x - 2 |}} ]_{\frac{3}{2}}^{\frac{5}{2}} $

$A = \ln \frac {\sqrt{| 5 - 6 |}}{\sqrt{| 5 - 2 |}} - \ln \frac {\sqrt{| 3 - 6 |}}{\sqrt{| 3 - 2 |}}$

$A = \ln \frac {1}{\sqrt{3}} - \ln \sqrt{3} $

$A = - 0.5493 - 0.5493 = - 1.0986 $

The actual answer is 0.235 $unit^2$

can anyone spot the error?