Question Number 212053 by universe last updated on 28/Sep/24
$$ \\ $$$$\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\int_{\mathrm{0}} ^{\:\boldsymbol{{y}}} \:\boldsymbol{{e}}^{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} } \boldsymbol{{dx}}\right)\boldsymbol{{dy}}\:+\int_{\mathrm{1}} ^{\mathrm{2}} \left(\int_{\mathrm{0}} ^{\:\mathrm{2}−\boldsymbol{{y}}} \:\boldsymbol{{e}}^{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} } \boldsymbol{{dx}}\right)\boldsymbol{{dy}}\:=\:? \\ $$$$ \\ $$
Answered by MrGaster last updated on 03/Nov/24
$$=\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{{y}} \left({e}^{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } {dx}\right){dy}+\int_{\mathrm{1}} ^{\mathrm{2}} \left(\int_{\mathrm{0}} ^{\mathrm{2}−{y}} {e}^{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } {dx}\right){dy} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{{y}} {e}^{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } {dxdy}+\int_{\mathrm{1}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\mathrm{2}−{y}} {e}^{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } {dxdy}\ldots \\ $$