Question Number 172178 by Mikenice last updated on 23/Jun/22
Answered by mr W last updated on 24/Jun/22
![=∫_0 ^1 x[((xy^2 )/2)+(y^3 /3)]_0 ^x dx =∫_0 ^1 ((5x^4 )/6)dx =[(x^5 /6)]_0 ^1 =(1/6)=God bless all!](Q172201.png)
$$=\int_{\mathrm{0}} ^{\mathrm{1}} {x}\left[\frac{{xy}^{\mathrm{2}} }{\mathrm{2}}+\frac{{y}^{\mathrm{3}} }{\mathrm{3}}\right]_{\mathrm{0}} ^{{x}} {dx} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{5}{x}^{\mathrm{4}} }{\mathrm{6}}{dx} \\ $$$$=\left[\frac{{x}^{\mathrm{5}} }{\mathrm{6}}\right]_{\mathrm{0}} ^{\mathrm{1}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{6}}={God}\:{bless}\:{all}! \\ $$