Challenging +1.2 This question requires integration of a rational function with a vertical asymptote in the integration domain, necessitating splitting the integral at the discontinuity (x=3/4) and careful handling of absolute values in logarithms. While the integration technique itself is standard A-level (partial fractions already done, standard ln form), the conceptual challenge of dealing with the asymptote and combining areas makes it moderately harder than average.
This is the graph of \(y = \frac{5}{4x-3} - \frac{3}{2}\)
\includegraphics{figure_6}
Find the area between the graph, the \(x\) axis, and the lines \(x = 1\) and \(x = 7\) in the form \(a \ln b + c\) where \(a,b,c \in Q\) [6]
This is the graph of $y = \frac{5}{4x-3} - \frac{3}{2}$
\includegraphics{figure_6}
Find the area between the graph, the $x$ axis, and the lines $x = 1$ and $x = 7$ in the form $a \ln b + c$ where $a,b,c \in Q$ [6]
\hfill \mbox{\textit{SPS SPS FM 2021 Q6 [6]}}