2022HSCShort answer

Q11 (b)

2 marks

Question

Evaluate $\displaystyle\int \sin^3(2x)\cos(2x)\,dx$ .

Try the question before revealing the answer.

Solution

Criteria	Marks
Provides correct solution	2
Chooses a suitable substitution, or equivalent merit	1

Sample answer:

\int \sin^3 2x\cos 2x\,dx =\frac14\int 4\sin^3 2x\cos 2x\,dx =\frac14\left(\frac{\sin^4(2x)}{2}\right)+C =\frac18\sin^4(2x)+C

Supplied marking guidance · human reviewed

Compare this with your working, not only your final sentence.

Syllabus alignment

Calculus

Further IntegrationApply substitution, partial fractions, integration by parts and recurrence relationships to theoretical and practical problems.

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