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Question Number 211006 by universe last updated on 26/Aug/24

Answered by mr W last updated on 26/Aug/24

$$=0becauseofoddfunction{zy}^2$$

Commented by mr W last updated on 26/Aug/24

$$youcouldalsohavemadeitlook$$$$morecomplicatedlike$$$$\int \int \underset{V}{\int }{zy}^2\sqrt{(1+x^2)(1+z^6)}dxdydz.$$$$buttheresultisalways0.$$

Commented by universe last updated on 26/Aug/24

$$sirwhatisthevalueinfirstoctant???$$

Commented by mr W last updated on 26/Aug/24

$$\int \int {\int }_D{zy}^{2}dxdydz$$$$={\int }_0^1{\int }_0^{\sqrt{1-x^2}}{y}^2{\int }_0^{\sqrt{1-x^2-y^2}}zdzdydx$$$$=\frac{1}{2}{\int }_0^1{\int }_0^{\sqrt{1-x^2}}{y}^2(1-x^2-y^2)dydx$$$$=\frac{1}{2}{\int }_0^1[\frac{{(1-x^2)}^4}{3}-\frac{{(1-x^2)}^5}{5}]dx$$$$=\frac{64}{945}-\frac{128}{3465}=\frac{64}{2079}✓$$

Commented by universe last updated on 27/Aug/24

$$thankyousir$$

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