Easy -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.
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)
---