| Exam Board | Edexcel |
|---|---|
| Module | C34 (Core Mathematics 3 & 4) |
| Year | 2018 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Areas by integration |
| Type | Area under curve with fractional/negative powers or roots |
| Difficulty | Standard +0.8 This question requires integration of a rational function with substitution (part a), then finding the intersection point of curve and line, and finally computing a volume of revolution using the difference of two functions squared. While the individual techniques are C3/C4 standard, the multi-step nature, need to find limits correctly, and algebraic manipulation of the volume integral (particularly simplifying the exact form) elevates this above a routine textbook exercise. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums1.08d Evaluate definite integrals: between limits1.08e Area between curve and x-axis: using definite integrals |
9.
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Diagram not drawn to scale
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\item Find
$$\int \frac { 1 } { ( 2 x - 1 ) ^ { 2 } } d x$$
Figure 2 shows a sketch of the curve with equation $y = \mathrm { f } ( x )$ where
$$f ( x ) = \frac { 12 } { ( 2 x - 1 ) } \quad 1 \leqslant x \leqslant 5$$
The finite region $R$, shown shaded in Figure 2, is bounded by the line with equation $x = 1$, the curve with equation $y = \mathrm { f } ( x )$ and the line with equation $y = \frac { 4 } { 3 }$.
The region $R$ is rotated through $2 \pi$ radians about the $x$-axis to form a solid of revolution.
\item Find the exact value of the volume of the solid generated, giving your answer in its simplest form.
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\section*{Leave \\
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\hfill \mbox{\textit{Edexcel C34 2018 Q9 [8]}}