Quick questions on Integrals giving inverse trig functions: $\arcsin$ , $\arctan$ and the patterns to recognise

3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is linear substitution shortcut?

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When the inside is linear,

bx + c

, you can quote the adjusted forms directly (the

\frac{1}{b}

comes from

du = b\,dx

What is sign confusion with

\arccos

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\int \frac{-1}{\sqrt{1 - x^2}} \, dx = \arccos x + C

. Most people prefer to keep

\arcsin

and handle the sign outside.

What are domain issues?

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\frac{1}{\sqrt{1 - x^2}}

is undefined for

|x| > 1

. A definite integral with limits outside

[-1, 1]

is invalid.

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