Standard +0.3 This is a straightforward area calculation requiring integration of 1/(2x+3) using substitution u=2x+3, finding intersection points, and subtracting a rectangular area. The substitution is standard, the algebra is routine, and the question clearly guides the student to the final form. Slightly above average due to requiring multiple steps (finding intersection, setting up correct limits, algebraic manipulation) but no novel insight needed.
3
\includegraphics[max width=\textwidth, alt={}, center]{a1ea242a-c7f4-46b0-b4b8-bd13b3880557-04_458_892_269_614}
The diagram shows part of the curve \(y = \frac { 6 } { 2 x + 3 }\). The shaded region is bounded by the curve and the lines \(x = 6\) and \(y = 2\).
Find the exact area of the shaded region, giving your answer in the form \(a - \ln b\), where \(a\) and \(b\) are integers.
3\\
\includegraphics[max width=\textwidth, alt={}, center]{a1ea242a-c7f4-46b0-b4b8-bd13b3880557-04_458_892_269_614}
The diagram shows part of the curve $y = \frac { 6 } { 2 x + 3 }$. The shaded region is bounded by the curve and the lines $x = 6$ and $y = 2$.
Find the exact area of the shaded region, giving your answer in the form $a - \ln b$, where $a$ and $b$ are integers.\\
\hfill \mbox{\textit{CAIE P2 2023 Q3 [5]}}