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Question
Which expression is an antiderivative of \[\frac{1}{\sqrt{1-x^2}}\]?
Options
\[\cos^{-1}x+\mathrm{C}\]
\[\tan^{-1}x+\mathrm{C}\]
\[\log|x|+\mathrm{C}\]
\[\sin^{-1}x+\mathrm{C}\]
MCQ
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Solution
The derivative of \(\sin^{-1}x\) is \(\frac{1}{\sqrt{1-x^2}}\). Therefore, \(\sin^{-1}x+\mathrm{C}\) is an antiderivative.
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