OCR C3 2009 January — Question 1 5 marks

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Year2009
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIntegration by Substitution
TypeIndefinite integral with linear substitution
DifficultyModerate -0.8 Both parts are routine integration exercises requiring direct application of standard results: (i) exponential integration with constant multiple, (ii) linear substitution or reverse chain rule. These are textbook drill questions with single-step solutions, significantly easier than the average A-level question which typically requires multi-step reasoning or combining multiple techniques.
Spec1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)1.08h Integration by substitution

1 Find
  1. \(\int 8 \mathrm { e } ^ { - 2 x } \mathrm {~d} x\),
  2. \(\int ( 4 x + 5 ) ^ { 6 } \mathrm {~d} x\).

1 Find\\
(i) $\int 8 \mathrm { e } ^ { - 2 x } \mathrm {~d} x$,\\
(ii) $\int ( 4 x + 5 ) ^ { 6 } \mathrm {~d} x$.

\hfill \mbox{\textit{OCR C3 2009 Q1 [5]}}