Moderate -0.8 This is a straightforward integration question requiring only the power rule for integration and evaluation at given limits. The algebraic manipulation with surds is routine for AS level. It's easier than average because it's a single-step 'show that' problem with no problem-solving or conceptual challenges beyond basic integration technique.
3 Show that the area of the region bounded by the curve \(y = 3 x ^ { - \frac { 3 } { 2 } }\), the lines \(x = 1 , x = 3\) and the \(x\)-axis is \(6 - 2 \sqrt { 3 }\).
Correct intermediate step using surds which follows from substitution of limits and is not identical to given answer and completion
\(6 - 2\sqrt{3}\) AG
[5]
## Question 3:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\int_1^3 3x^{-\frac{3}{2}}\,dx$ | M1 (1.1a) | Attempt to integrate (ignore missing limits) | Do not award any A-marks if M0 is given |
| $\left[-6x^{-\frac{1}{2}}\right]_1^3$ | A1 (1.1) | Correct integration | |
| | A1 (1.1) | Correct limits seen at some point | |
| $\frac{-6}{\sqrt{3}} - \frac{-6}{\sqrt{1}}$ | M1 (1.1) | Substitution of limits (condone one error) | |
| $\frac{-6}{\sqrt{3}} + 6$ | E1 (2.1) | Correct intermediate step using surds which follows from substitution of limits and is not identical to given answer and completion | Given answer must be seen to score E1 |
| $6 - 2\sqrt{3}$ AG | | |
| **[5]** | | |
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3 Show that the area of the region bounded by the curve $y = 3 x ^ { - \frac { 3 } { 2 } }$, the lines $x = 1 , x = 3$ and the $x$-axis is $6 - 2 \sqrt { 3 }$.
\hfill \mbox{\textit{OCR MEI AS Paper 2 Q3 [5]}}