Solve. ${\int}_{0}{\ufeff}^{1}\prod (\sqrt{\mathrm{cos}(\prod y/4)}{)}^{2}dy$

Shannon Andrews
2022-07-27
Answered

Solve. ${\int}_{0}{\ufeff}^{1}\prod (\sqrt{\mathrm{cos}(\prod y/4)}{)}^{2}dy$

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encoplemt5

Answered 2022-07-28
Author has **15** answers

${\int}_{0}^{1}\prod (\sqrt{\mathrm{cos}(\prod y/4)}{)}^{2}dy$

$={\int}_{0}^{1}\prod \mathrm{cos}\frac{\prod y}{4}dy$

$=\prod {\int}_{0}^{1}\mathrm{cos}\frac{\prod y}{4}dy$

$=\prod \frac{\mathrm{sin}\frac{\prod y}{4}}{\frac{\prod}{4}}{]}_{0}^{1}$

$=4[\mathrm{sin}\frac{\prod}{4}-\mathrm{sin}0]$

$=4[\frac{1}{\sqrt{2}}-0]$

$=4\frac{1}{\sqrt{2}}$

$=\frac{4\sqrt{2}}{2}=2\sqrt{2}$

$={\int}_{0}^{1}\prod \mathrm{cos}\frac{\prod y}{4}dy$

$=\prod {\int}_{0}^{1}\mathrm{cos}\frac{\prod y}{4}dy$

$=\prod \frac{\mathrm{sin}\frac{\prod y}{4}}{\frac{\prod}{4}}{]}_{0}^{1}$

$=4[\mathrm{sin}\frac{\prod}{4}-\mathrm{sin}0]$

$=4[\frac{1}{\sqrt{2}}-0]$

$=4\frac{1}{\sqrt{2}}$

$=\frac{4\sqrt{2}}{2}=2\sqrt{2}$

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