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Question Number 8632 by swapnil last updated on 19/Oct/16
evaluate  ∫_0 ^3 ∫_0 ^4 1+x dy dx
$${evaluate} \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\mathrm{1}+{x}\:{dy}\:{dx} \\ $$$$\: \\ $$
Answered by FilupSmith last updated on 19/Oct/16
∫_0 ^3 ∫_0 ^4 1+x dy dx  =∫_0 ^3 (y+yx)∣_0 ^4 dx  =∫_0 ^3 (4+4x)dx  =(4x+2x^2 )∣_0 ^3   =(12+18)  =30
$$\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\mathrm{1}+{x}\:{dy}\:{dx} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{3}} \left({y}+{yx}\right)\mid_{\mathrm{0}} ^{\mathrm{4}} {dx} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{3}} \left(\mathrm{4}+\mathrm{4}{x}\right){dx} \\ $$$$=\left(\mathrm{4}{x}+\mathrm{2}{x}^{\mathrm{2}} \right)\mid_{\mathrm{0}} ^{\mathrm{3}} \\ $$$$=\left(\mathrm{12}+\mathrm{18}\right) \\ $$$$=\mathrm{30} \\ $$

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