Moderate -0.3 This is a straightforward two-part question testing standard partial fractions technique with linear factors and subsequent integration. Part (i) is routine algebraic manipulation, and part (ii) requires integrating logarithmic terms and simplifying—all standard C4 content with no novel problem-solving required. Slightly easier than average due to the predictable structure and well-practiced techniques.
3. (i) Express \(\frac { x + 11 } { ( x + 4 ) ( x - 3 ) }\) as a sum of partial fractions.
(ii) Evaluate
$$\int _ { 0 } ^ { 2 } \frac { x + 11 } { ( x + 4 ) ( x - 3 ) } d x$$
giving your answer in the form \(\ln k\), where \(k\) is an exact simplified fraction.
3. (i) Express $\frac { x + 11 } { ( x + 4 ) ( x - 3 ) }$ as a sum of partial fractions.\\
(ii) Evaluate
$$\int _ { 0 } ^ { 2 } \frac { x + 11 } { ( x + 4 ) ( x - 3 ) } d x$$
giving your answer in the form $\ln k$, where $k$ is an exact simplified fraction.\\
\hfill \mbox{\textit{OCR C4 Q3 [7]}}