| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2009 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Areas by integration |
| Type | Deduce related integral from numerical approximation |
| Difficulty | Moderate -0.5 Part (i) is a standard Simpson's rule application with straightforward function values. Part (ii) requires recognizing that ln(x^10) = 10ln(x), making it a simple multiplication of the part (i) answer. This is routine calculus manipulation with no conceptual difficulty beyond basic logarithm laws, making it slightly easier than average. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.09f Trapezium rule: numerical integration |
2 (i) Use Simpson's rule with four strips to find an approximation to
$$\int _ { 4 } ^ { 12 } \ln x \mathrm {~d} x$$
giving your answer correct to 2 decimal places.\\
(ii) Deduce an approximation to $\int _ { 4 } ^ { 12 } \ln \left( x ^ { 10 } \right) \mathrm { d } x$.
\hfill \mbox{\textit{OCR C3 2009 Q2 [5]}}