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Question
\[\int\limits_0^1 \cos^{- 1} x dx\]
Solution
\[\int_0^1 \cos^{- 1} x d x\]
\[ = \int_0^1 \left( \cos^{- 1} x \times 1 \right) d x\]
\[ = \left[ \cos^{- 1} x x \right]_0^1 - \int_0^1 \frac{- x}{\sqrt{1 - x^2}}dx\]
\[ = \left[ x \cos^{- 1} x \right]_0^1 - \frac{2}{2} \left[ \sqrt{1 - x^2} \right]_0^1 \]
\[ = 0 + 1\]
\[ = 1\]
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