OCR C4 — Question 3 8 marks

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIntegration by Parts
TypeIndependent multi-part (different techniques)
DifficultyStandard +0.3 Part (i) is a standard substitution (u = 2 - x²) requiring recognition of the derivative in the numerator. Part (ii) requires integration by parts applied twice, which is a routine C4 technique. Both are textbook exercises with no novel insight required, making this slightly easier than average.
Spec1.08h Integration by substitution1.08i Integration by parts

3. Find
  1. \(\int \frac { x } { 2 - x ^ { 2 } } \mathrm {~d} x\),
  2. \(\int x ^ { 2 } \mathrm { e } ^ { - x } \mathrm {~d} x\).

3. Find\\
(i) $\int \frac { x } { 2 - x ^ { 2 } } \mathrm {~d} x$,\\
(ii) $\int x ^ { 2 } \mathrm { e } ^ { - x } \mathrm {~d} x$.\\

\hfill \mbox{\textit{OCR C4  Q3 [8]}}