Edexcel C2 2007 June — Question 1 4 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2007
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypeShow definite integral equals value
DifficultyModerate -0.8 This is a straightforward C2 integration question requiring only the power rule (rewriting x^(-1/2) as x^(-1/2), integrating to get 2x^(1/2)) and substituting limits. The algebraic manipulation to express the answer in the required form a + b√2 is routine. Below average difficulty as it's a standard single-technique question with no problem-solving element.
Spec1.08b Integrate x^n: where n != -1 and sums1.08d Evaluate definite integrals: between limits
Evaluate \(\int _ { 1 } ^ { 8 } \frac { 1 } { \sqrt { } x } \mathrm {~d} x\), giving your answer in the form \(a + b \sqrt { } 2\), where \(a\) and \(b\) are integers.
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(\int x^{-\frac{1}{2}}\,dx = \dfrac{x^{\frac{1}{2}}}{\frac{1}{2}}\)M1 A1 Or equivalent such as \(2x^{\frac{1}{2}}\) or \(2\sqrt{x}\)
\(\left[\dfrac{x^{\frac{1}{2}}}{\frac{1}{2}}\right]_1^8 = 2\sqrt{8} - 2 = -2 + 4\sqrt{2}\)M1 A1 Or \(4\sqrt{2}-2\), or \(2(2\sqrt{2}-1)\), or \(2(-1+2\sqrt{2})\)
Total: 4 marks
# Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\int x^{-\frac{1}{2}}\,dx = \dfrac{x^{\frac{1}{2}}}{\frac{1}{2}}$ | M1 A1 | Or equivalent such as $2x^{\frac{1}{2}}$ or $2\sqrt{x}$ |
| $\left[\dfrac{x^{\frac{1}{2}}}{\frac{1}{2}}\right]_1^8 = 2\sqrt{8} - 2 = -2 + 4\sqrt{2}$ | M1 A1 | Or $4\sqrt{2}-2$, or $2(2\sqrt{2}-1)$, or $2(-1+2\sqrt{2})$ |

**Total: 4 marks**

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Evaluate $\int _ { 1 } ^ { 8 } \frac { 1 } { \sqrt { } x } \mathrm {~d} x$, giving your answer in the form $a + b \sqrt { } 2$, where $a$ and $b$ are integers.\\

\hfill \mbox{\textit{Edexcel C2 2007 Q1 [4]}}
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