OCR MEI C3 2009 January — Question 4 5 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Year2009
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIntegration by Substitution
TypeDefinite integral with simple linear/polynomial substitution
DifficultyModerate -0.3 This is a straightforward integration by substitution question with a simple linear expression under the square root. The substitution u = 1 + 4x is obvious, the limits transform easily, and the resulting integral ∫√u du is standard. While it requires proper technique and care with the factor of 4, it's slightly easier than average as it's a single-step method application with no conceptual challenges.
Spec1.08h Integration by substitution

4 Find the exact value of \(\int _ { 0 } ^ { 2 } \sqrt { 1 + 4 x } \mathrm {~d} x\), showing your working.

4 Find the exact value of $\int _ { 0 } ^ { 2 } \sqrt { 1 + 4 x } \mathrm {~d} x$, showing your working.

\hfill \mbox{\textit{OCR MEI C3 2009 Q4 [5]}}