2023HSCShort answer

Q11 (d)

2 marks

Question

Find

\int \frac{1}{\sqrt{4-9x^2}}\,dx.

Try the question before revealing the answer.

Solution

Criteria	Marks
Provides correct solution	2
Attempts to rewrite the integrand in a suitable form, or equivalent merit	1

Sample answer:

\int \frac{1}{\sqrt{4-9x^2}}\,dx =\frac{1}{3}\int\frac{3}{\sqrt{2^2-(3x)^2}}\,dx

=\frac{1}{3}\sin^{-1}\left(\frac{3x}{2}\right)+C

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Syllabus alignment

Calculus

Further Calculus SkillsApply integration by substitution, trigonometric integrals and derivatives of inverse functions, including inverse trigonometric functions.

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