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Question Number 37235 by abdo.msup.com last updated on 11/Jun/18

calculate ∫_0 ^(π/2) (√(4sin^2 t +cos^2 (t)))  dt

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \sqrt{\mathrm{4}{sin}^{\mathrm{2}} {t}\:+{cos}^{\mathrm{2}} \left({t}\right)}\:\:{dt} \\ $$

Answered by tanmay.chaudhury50@gmail.com last updated on 11/Jun/18

∫_0 ^(Π/2) (√((((4(1+cos2t))/2)+((1−cos2t)/2))/))dt  ∫_0 ^(Π/2) (√(2+2cos2t+(1/2)−cos2t dt))  ∫_0 ^(Π/2) (√((5/2)+cos2t )) dt  contd

$$\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} \sqrt{\frac{\frac{\mathrm{4}\left(\mathrm{1}+{cos}\mathrm{2}{t}\right)}{\mathrm{2}}+\frac{\mathrm{1}−{cos}\mathrm{2}{t}}{\mathrm{2}}}{}}{dt} \\ $$$$\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} \sqrt{\mathrm{2}+\mathrm{2}{cos}\mathrm{2}{t}+\frac{\mathrm{1}}{\mathrm{2}}−{cos}\mathrm{2}{t}\:{dt}} \\ $$$$\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} \sqrt{\frac{\mathrm{5}}{\mathrm{2}}+{cos}\mathrm{2}{t}\:}\:{dt} \\ $$$${contd} \\ $$$$ \\ $$

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