| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Trapezium rule with stated number of strips |
| Difficulty | Moderate -0.8 This is a straightforward application of the trapezium rule with clearly specified strips (n=4, interval [0,2]), followed by a simple volume calculation using scaling. The function is easy to evaluate, and both parts require only routine procedural work with no problem-solving insight needed. |
| Spec | 1.09f Trapezium rule: numerical integration |
4.\\
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The diagram shows the curve with equation $y = \frac { 1 } { x ^ { 2 } + 1 }$.\\
The shaded region $R$ is bounded by the curve, the coordinate axes and the line $x = 2$.\\
(i) Use the trapezium rule with four strips of equal width to estimate the area of $R$.
The cross-section of a support for a bookshelf is modelled by $R$ with 1 unit on each axis representing 8 cm . Given that the support is 2 cm thick,\\
(ii) find an estimate for the volume of the support.\\
\hfill \mbox{\textit{OCR C2 Q4 [7]}}