MEX-C1
Further Integration
Integrate using trigonometric substitution, partial fractions with irreducible quadratics, and integration by parts.
Sample questions
- 1.Use the substitution x = 2sinθ to evaluate ∫ 1/√(4 − x²) dx.
- 2.Find ∫ (3x)/(x² + 1)(x − 2) dx using partial fractions.
Exam weighting
5–8 marks — the most heavily-weighted single topic.
Common student mistakes
- ·Selecting the wrong trigonometric substitution for the integrand form
- ·Errors in setting up partial fractions for irreducible quadratics
- ·Forgetting to back-substitute to the original variable
MEX-C2
Applications of Integration
Find volumes of solids of revolution; apply arc length and surface area integrals.
Sample questions
- 1.Find the volume of the solid formed by rotating y = √x about the x-axis for 0 ≤ x ≤ 4.
Exam weighting
4–6 marks.
Common student mistakes
- ·Forgetting to square the function when computing a volume of revolution
- ·Incorrect limits of integration when the curve is rotated about the y-axis
Other Extension 2 topics
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