Question Number 170980 by anas_zaidan last updated on 05/Jun/22
Answered by aleks041103 last updated on 05/Jun/22
$$\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}^{\mathrm{2}} {ydxdy}= \\ $$$$=\left(\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}^{\mathrm{2}} {dx}\right)\left(\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}{ydy}\right)= \\ $$$$=\left(\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{0}}{\mathrm{3}}\right)\left(\frac{\mathrm{4}^{\mathrm{2}} −\mathrm{2}^{\mathrm{2}} }{\mathrm{2}}\right)= \\ $$$$=\frac{\mathrm{1}}{\mathrm{6}}\left(\mathrm{16}−\mathrm{4}\right)=\mathrm{2} \\ $$