| Exam Board | OCR |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2008 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Rectangle bounds for definite integral |
| Difficulty | Standard +0.3 This is a straightforward application of lower and upper Riemann sums using rectangles to bound a definite integral. Part (i) requires simple geometric reasoning (comparing area to rectangles of width 1), while part (ii) is computational but routine—evaluating the function at 5 or 6 points and summing. The concept is standard for FP2 numerical methods, requiring no novel insight beyond applying the rectangle method correctly. |
| Spec | 1.09f Trapezium rule: numerical integration |
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The diagram shows the curve with equation $y = \sqrt { 1 + x ^ { 3 } }$, for $2 \leqslant x \leqslant 3$. The region under the curve between these limits has area $A$.\\
(i) Explain why $3 < A < \sqrt { 28 }$.\\
(ii) The region is divided into 5 strips, each of width 0.2 . By using suitable rectangles, find improved lower and upper bounds between which $A$ lies. Give your answers correct to 3 significant figures.
\hfill \mbox{\textit{OCR FP2 2008 Q3 [6]}}