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Year 12 Maths Extension 1 (2027) Calculus

Integration giving inverse trig functions

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Question 1
182781

Which expression is equal to \(\displaystyle\int\dfrac{dx}{\sqrt{a^2-x^2}}\)?

A.
\(\sin^{-1}\dfrac{x}{a}+C\)
B.
\(\dfrac{1}{a}\sin^{-1}\dfrac{x}{a}+C\)
C.
\(\cos^{-1}\dfrac{x}{a}+C\)
D.
\(\dfrac{1}{a}\tan^{-1}\dfrac{x}{a}+C\)
\(\sin^{-1}\dfrac{x}{a}+C\)

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