Mathematics

Solve : 
$$\int {{{\sin }^{ - 1}}\left( {\cos x} \right)dx} $$


SOLUTION
$$\begin{array}{l} \int { { { \sin   }^{ -1 } }\left( { \cos  x } \right) dx }  \\ =\int { { { \sin   }^{ -1 } }\left\{ { \sin  \left( { \frac { \pi  }{ 2 } -x } \right)  } \right\} dx }  \\ =\int { \left( { \frac { \pi  }{ 2 } -x } \right) dx }  \\ =\frac { \pi  }{ 2 } .\int { dx } -\int { xdx }  \\ =\frac { { \pi x } }{ 2 } -\frac { { { x^{ 2 } } } }{ 2 } +C \end{array}$$
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Subjective Medium Published on 17th 09, 2020
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