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 itself is standard C4 technique, recognizing the need to split the integral and correctly managing signs when the function is negative requires solid understanding beyond routine application.
This is the graph of \(y = \frac{5}{4x-3} - \frac{3}{2}\)
\includegraphics{figure_7}
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_7}
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 Q7 [6]}}