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
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