Question Number 121707 by rs4089 last updated on 11/Nov/20
Answered by Dwaipayan Shikari last updated on 11/Nov/20
![∫_1 ^2 ∫_1 ^3 xy^2 dxdy ∫_1 ^2 y^2 [(x^2 /2)]_1 ^3 dy =(8/2)∫_1 ^2 y^2 dy=4((8/3)−(1/3))=((28)/3)=9.33333](https://www.tinkutara.com/question/Q121710.png)
$$\int_{\mathrm{1}} ^{\mathrm{2}} \int_{\mathrm{1}} ^{\mathrm{3}} {xy}^{\mathrm{2}} {dxdy} \\ $$$$\int_{\mathrm{1}} ^{\mathrm{2}} {y}^{\mathrm{2}} \left[\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\right]_{\mathrm{1}} ^{\mathrm{3}} {dy} \\ $$$$=\frac{\mathrm{8}}{\mathrm{2}}\int_{\mathrm{1}} ^{\mathrm{2}} {y}^{\mathrm{2}} {dy}=\mathrm{4}\left(\frac{\mathrm{8}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{3}}\right)=\frac{\mathrm{28}}{\mathrm{3}}=\mathrm{9}.\mathrm{33333} \\ $$