CAIE IGCSE Additional Math 14.10 Understand Integration As Reverse Differentiation Questions

Practise selecting and applying integration by parts to products, exponentials, logarithms and trigonometric expressions in Cambridge Additional Mathematics problems.

Exam points

Evaluate integrals using integration by parts, including choices of parts and repeated applications where needed.

[Maximum number: 4]

Hence find $\int x \sin 2 x \mathrm{~d} x$ .

$-\frac12x\cos2x+\frac14\sin2x+c$ oe, isw, nfww
M3 for $-\frac12x\cos2x+\frac14\sin2x$ or equivalent integration-by-parts working;
M2/M1 for partial correct working as in markscheme.
A1

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CAIE IGCSE Additional Math 14.10 Understand Integration As Reverse Differentiation Questions question 1