Mathematics

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

$\sin x - \cos x + c$

##### 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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

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