Mathematics

$$\int \sqrt{1 +\sin2x} dx$$ is


ANSWER

$$\sin x - \cos x + c$$


SOLUTION
Given:
$$ \int { \sqrt { 1+\sin { 2x }  } dx } $$
 solution;
$$ 1+\sin  2x=\sin ^{ 2 }{ x } +\cos ^{ 2 }{ x } +2\sin { x } \cos { x } \\ ={ \left( \sin { x } +\cos { x }  \right)  }^{ 2 }\\ I=\int { \sqrt { 1+\sin { 2x }  } dx } =\int { \sqrt { \left( \sin { x } +\cos { x }  \right) ^{ 2 } } dx } \\ I=\int { (\sin { x } +\cos { x } )dx } \\ =-\cos { x } +\sin { x } +C$$
 Hence the correct answer is
$$ \sin { x } -\cos { x } +C$$
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Single Correct Medium Published on 17th 09, 2020
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