Mathematics

# Prove that $\displaystyle \int_0^{\frac{{32\pi }}{3}} {\sqrt {1 + \cos 2x} } {\rm{ }}dx = 22\sqrt 2 - \sqrt {\frac{3}{2}}$

##### SOLUTION
${I_1} = \int_{10\pi }^{32\pi /2} {|\cos x|dx}$
$= \int_0^{2\pi /3} {|\cos x\backslash dx}$
$= 2 - \dfrac{{\sqrt 3 }}{2}$
$I = 20\sqrt 2 + \sqrt 2 |2 - \dfrac{{\sqrt 3 }}{2}$
$= 20\sqrt 2 + 2\sqrt 2 - \dfrac{{\sqrt 3 \sqrt 2 }}{2}$
$= 22\sqrt 2 - \sqrt {\dfrac{3}{2}}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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