WJEC Unit 3 2022 June — Question 18

Exam BoardWJEC
ModuleUnit 3 (Unit 3)
Year2022
SessionJune
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Mark schemeDownload PDF ↗
TopicIntegration by Substitution
TypeDefinite integral with complex substitution requiring algebraic rearrangement
DifficultyStandard +0.3 This is a straightforward integration by substitution question with the natural choice u = x + 3, requiring algebraic manipulation to express x² in terms of u, followed by routine integration of polynomial terms and application of limits. While it requires multiple steps and careful algebra, it follows a standard pattern for this topic with no novel insight needed.
Spec1.08d Evaluate definite integrals: between limits1.08h Integration by substitution
a) Use a suitable substitution to find $$\int \frac { x ^ { 2 } } { ( x + 3 ) ^ { 4 } } \mathrm {~d} x$$ b) Hence evaluate \(\int _ { 0 } ^ { 1 } \frac { x ^ { 2 } } { ( x + 3 ) ^ { 4 } } \mathrm {~d} x\). END OF PAPER \end{document} 
a) Use a suitable substitution to find

$$\int \frac { x ^ { 2 } } { ( x + 3 ) ^ { 4 } } \mathrm {~d} x$$

b) Hence evaluate $\int _ { 0 } ^ { 1 } \frac { x ^ { 2 } } { ( x + 3 ) ^ { 4 } } \mathrm {~d} x$.

END OF PAPER

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\hfill \mbox{\textit{WJEC Unit 3 2022 Q18}}
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