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Question Number 190984 by Spillover last updated on 15/Apr/23

$$$$$${\int }_0^3{\int }_0^2{\mathrm{x}}^2\mathrm{ydydx}$$$$$$

Answered by a.lgnaoui last updated on 15/Apr/23

$${\int }_0^3{\int }_0^2{\mathrm{x}}^2\mathrm{ydydx}={\int }_0^3{\mathrm{x}}^2\mathrm{dx}{\int }_0^2\mathrm{ydy}={\left[\frac{{\mathrm{x}}^3}{3}\right]}_0^3\times {\left[\frac{{\mathrm{y}}^2}{2}\right]}_0^2$$$$=9\times 2=18$$

Answered by gungun last updated on 16/Apr/23

$${\int }_0^3\left(\frac{1}{2}{x}^2{y}^2\right)dx$$$$={\int }_0^3{\left(\frac{1}{2}{x}^2{y}^2\right]}_0^{2}dx$$$$={\int }_0^3\left(2x^2\right)dx$$$$={\left(\frac{2}{3}{x}^3\right]}_0^3=\frac{2}{3}\times 3^3=9\times 2=18$$$$$$

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