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let-I-0-pi-2-sinx-1-sinxcosx-dx-and-J-0-pi-2-cosx-1-sinx-cosx-dx-1-calculate-I-J-2-find-I-and-J-




Question Number 30185 by abdo imad last updated on 17/Feb/18
let  I= ∫_0 ^(π/2)      ((sinx)/( (√(1+sinxcosx))))dx and  J= ∫_0 ^(π/2)    ((cosx)/( (√(1+sinx cosx)))) dx  1) calculate I +J  2) find I and J.
$${let}\:\:{I}=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{sinx}}{\:\sqrt{\mathrm{1}+{sinxcosx}}}{dx}\:{and} \\ $$$${J}=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{cosx}}{\:\sqrt{\mathrm{1}+{sinx}\:{cosx}}}\:{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}\:+{J} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{I}\:{and}\:{J}. \\ $$

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