Question 1 - A-Level Maths

Exam Board	CAIE
Module	P1 (Pure Mathematics 1)
Year	2011
Session	June
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Indefinite & Definite Integrals
Type	Basic indefinite integration
Difficulty	Easy -1.2 This is a straightforward application of the power rule for integration requiring only direct recall of standard formulas. The question involves two simple terms with no algebraic manipulation, substitution, or problem-solving—just routine integration of x^3 and x^(-3), making it easier than average.
Spec	1.08b Integrate x^n: where n != -1 and sums

Find \(\int \left(x^3 + \frac{1}{x^3}\right) \mathrm{d}x\). [3]

Answer	Marks	Guidance
\(\int\left(x^3 + \frac{1}{x^3}\right)dx = \frac{x^4}{4} + \frac{x^{-2}}{-2} + c\)	3 × B1	Allow unsimplified, 1 mark for each term, including "\(c\)"

$\int\left(x^3 + \frac{1}{x^3}\right)dx = \frac{x^4}{4} + \frac{x^{-2}}{-2} + c$ | 3 × B1 | Allow unsimplified, 1 mark for each term, including "$c$"

Find $\int \left(x^3 + \frac{1}{x^3}\right) \mathrm{d}x$. [3]

\hfill \mbox{\textit{CAIE P1 2011 Q1 [3]}}