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Category: Integration

Compute-the-volume-bounded-by-the-surfaces-y-x-2-x-y-2-z-0-z-12-y-x-2-Ans-549-144-

Question Number 20281 by ajfour last updated on 25/Aug/17 $${Compute}\:{the}\:{volume}\:{bounded}\:{by} \\ $$$${the}\:{surfaces}:\:{y}={x}^{\mathrm{2}} ,\:{x}={y}^{\mathrm{2}} ,\:{z}=\mathrm{0}, \\ $$$${z}=\mathrm{12}+{y}−{x}^{\mathrm{2}} .\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\:{Ans}.\:\:\:\:\frac{\mathrm{549}}{\mathrm{144}}\right] \\ $$ Terms of Service Privacy…

x-2-1-x-2-dx-

Question Number 85813 by jagoll last updated on 25/Mar/20 $$\int\:\mathrm{x}^{\mathrm{2}} \:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:? \\ $$ Commented by jagoll last updated on 25/Mar/20 $$\int\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\:\left(\mathrm{2x}\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\right)\:\mathrm{dx}\:=\: \\ $$$$\int\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}}…

dx-x-x-x-pi-where-gt-0-

Question Number 151341 by peter frank last updated on 20/Aug/21 $$\int_{\alpha} ^{\beta} \frac{\mathrm{dx}}{\mathrm{x}\sqrt{\left(\mathrm{x}−\alpha\right)\left(\beta−\mathrm{x}\right)\:}}=\frac{\pi}{\:\sqrt{\alpha\beta}} \\ $$$$\mathrm{where}\:\alpha,\beta\:>\mathrm{0} \\ $$ Answered by Kamel last updated on 20/Aug/21 $$…

0-1-x-2-dx-1-x-4-

Question Number 85807 by jagoll last updated on 25/Mar/20 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{x}^{\mathrm{2}} \:\mathrm{dx}}{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }} \\ $$ Answered by Joel578 last updated on 25/Mar/20 $${I}\:\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}}…

dx-1-x-1-x-

Question Number 20257 by tammi last updated on 24/Aug/17 $$\int\frac{{dx}}{\left(\mathrm{1}−{x}\right)\sqrt{\mathrm{1}+{x}}} \\ $$ Answered by Tinkutara last updated on 24/Aug/17 $${t}^{\mathrm{2}} \:=\:{x}\:+\:\mathrm{1} \\ $$$${dx}\:=\:\mathrm{2}{tdt} \\ $$$$\int\frac{\mathrm{2}{tdt}}{\left(\mathrm{2}\:−\:{t}^{\mathrm{2}}…