Question Number 8632 by swapnil last updated on 19/Oct/16
$${evaluate} \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\mathrm{1}+{x}\:{dy}\:{dx} \\ $$$$\: \\ $$
Answered by FilupSmith last updated on 19/Oct/16
$$\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\mathrm{1}+{x}\:{dy}\:{dx} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{3}} \left({y}+{yx}\right)\mid_{\mathrm{0}} ^{\mathrm{4}} {dx} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{3}} \left(\mathrm{4}+\mathrm{4}{x}\right){dx} \\ $$$$=\left(\mathrm{4}{x}+\mathrm{2}{x}^{\mathrm{2}} \right)\mid_{\mathrm{0}} ^{\mathrm{3}} \\ $$$$=\left(\mathrm{12}+\mathrm{18}\right) \\ $$$$=\mathrm{30} \\ $$