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Question Number 115364 by Bird last updated on 25/Sep/20

$$calculate\int {\int }_{{[0,1]}^2}\sqrt{xy}(x^2+y^2)dxdy$$

Answered by Olaf last updated on 25/Sep/20

$$\int {\int }_{{[0,1]}^2}(\sqrt{y}{x}^{5/2}+y^{5/2}\sqrt{x})dxdy$$$$={\int }_0^1{[\frac{2}{7}\sqrt{y}{x}^{7/2}+\frac{2}{3}{y}^{5/2}{x}^{3/2}]}_0^{1}dy$$$$={\int }_0^1(\frac{2}{7}\sqrt{y}+\frac{2}{3}{y}^{5/2})dy$$$$={[\frac{2}{7}\times \frac{2}{3}{y}^{3/2}+\frac{2}{3}\times \frac{2}{7}{y}^{7/2}]}_0^1$$$$=\frac{8}{21}$$

Commented by mathmax by abdo last updated on 25/Sep/20

$$\mathrm{thank}\mathrm{you}\mathrm{sir}$$

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