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Category: Integration

Question-170593

Question Number 170593 by 119065 last updated on 27/May/22 Commented by mkam last updated on 27/May/22 $$\int\:\left({x}+\mathrm{3}\:−\:\mathrm{3}\right)\:\left({x}+\mathrm{3}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} {dx}=\int\:\left({x}+\mathrm{3}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} −\mathrm{3}\left({x}+\mathrm{3}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} {dx} \\ $$$$ \\ $$$$=\:\frac{\mathrm{2}}{\mathrm{5}}\:\left({x}+\mathrm{3}\right)^{\frac{\mathrm{5}}{\mathrm{2}}} \:−\:\mathrm{2}\:\left({x}+\mathrm{3}\right)^{\frac{\mathrm{3}}{\mathrm{2}}}…

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Question Number 170545 by kndramaths last updated on 26/May/22 $$\:\:\:\:{please}\:{help}\:{me}\:{to}\:{find}\:{this}. \\ $$$$\:\:\:{a}=\:\int\int_{{D}} \frac{{ydxdy}}{{a}^{\mathrm{2}} +{x}^{\mathrm{2}} }\:{D}:\left\{{x}\geqslant\mathrm{0}.{y}\geqslant\mathrm{0}.{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \leqslant{a}^{\mathrm{2}} \right\} \\ $$$$\:\:\:{b}=\int\int\int_{{v}} \left({x}−{y}+{z}\right)^{\mathrm{2}} {dxdydz} \\ $$$$\:\:{v}:\left\{{x}=\mathrm{0}.{y}=\mathrm{0}.{z}=\mathrm{0}\:{x}+{z}=\mathrm{1}.{y}+{z}=\mathrm{1}\right\} \\…