Mathematics

# $\int _{ 0 }^{ 400\pi }{ \sqrt { 1-\cos { 2x } } }$

$800\sqrt 2$

##### SOLUTION
$I=\int _{ 0 }^{ 400\pi }{ \sqrt { 1-\cos x } dx } \\ =400\int _{ 0 }^{ \pi }{ \sqrt { 1-\cos 2x } dx } \\ =800\int _{ 0 }^{ \pi }{ \sqrt { 2 } \sqrt { { { \sin }^{ 2 } }x } dx } \\ =800\sqrt { 2 } \int _{ 0 }^{ \frac { \pi }{ 2 } }{ \sin xdx } \\ =800\sqrt { 2 } \left[ { \cos x } \right] _{ \frac { \pi }{ 2 } }^{ 0 } \\ =800\sqrt { 2 }$

$\\ Hence,\, the\, option\, C\, is\, the\, correct\, answer.$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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