Edexcel C1 2009 January — Question 2 4 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2009
SessionJanuary
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStandard Integrals and Reverse Chain Rule
TypeFind indefinite integral of polynomial/power
DifficultyEasy -1.8 This is a straightforward application of the power rule for integration to a polynomial with three terms. It requires only direct recall of the formula ∫x^n dx = x^(n+1)/(n+1) + c with no problem-solving, making it significantly easier than average and typical of basic C1 integration exercises.
Spec1.08b Integrate x^n: where n != -1 and sums

Find \(\int \left( 12 x ^ { 5 } - 8 x ^ { 3 } + 3 \right) \mathrm { d } x\), giving each term in its simplest form.

Question 2:
AnswerMarks Guidance
\((I =)\frac{12}{6}x^6 - \frac{8}{4}x^4 + 3x + c\)M1 Attempt to integrate \(x^n \to x^{n+1}\), i.e. \(ax^6\) or \(ax^4\) or \(ax\). Also scored for \(+c\) alone.
\(= 2x^6 - 2x^4 + 3x + c\)A1, A1, A1 1st A1 for \(2x^6\); 2nd A1 for \(-2x^4\); 3rd A1 for \(3x + c\). Allow \(3x^1 + c\) but not \(\frac{3x^1}{1}+c\). All A marks dependent on M mark. ([4] total)
## Question 2:

$(I =)\frac{12}{6}x^6 - \frac{8}{4}x^4 + 3x + c$ | M1 | Attempt to integrate $x^n \to x^{n+1}$, i.e. $ax^6$ or $ax^4$ or $ax$. Also scored for $+c$ alone.

$= 2x^6 - 2x^4 + 3x + c$ | A1, A1, A1 | 1st A1 for $2x^6$; 2nd A1 for $-2x^4$; 3rd A1 for $3x + c$. Allow $3x^1 + c$ but not $\frac{3x^1}{1}+c$. All A marks dependent on M mark. (**[4]** total)

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Find $\int \left( 12 x ^ { 5 } - 8 x ^ { 3 } + 3 \right) \mathrm { d } x$, giving each term in its simplest form.\\

\hfill \mbox{\textit{Edexcel C1 2009 Q2 [4]}}