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Category: Integration

Question-44092

Question Number 44092 by peter frank last updated on 21/Sep/18 Commented by maxmathsup by imad last updated on 21/Sep/18 $${let}\:{I}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)}\:\:{changement}\:{x}\:={sh}\left({t}\right)\:{give}\: \\ $$$${I}\:=\:\int_{\mathrm{0}}…

If-f-x-continue-in-1-30-and-6-30-f-x-dx-30-then-1-9-f-3y-3-dy-

Question Number 109546 by bemath last updated on 24/Aug/20 $${If}\:{f}\left({x}\right)\:{continue}\:{in}\:\left[\:\mathrm{1},\mathrm{30}\right]\:{and}\: \\ $$$$\underset{\mathrm{6}} {\overset{\mathrm{30}} {\int}}{f}\left({x}\right){dx}\:=\:\mathrm{30},\:{then}\:\underset{\mathrm{1}} {\overset{\mathrm{9}} {\int}}{f}\left(\mathrm{3}{y}+\mathrm{3}\right){dy}\:=\:\_\_ \\ $$ Commented by kaivan.ahmadi last updated on 24/Aug/20…

1-x-1-2-x-1-3-dx-

Question Number 43991 by Tawa1 last updated on 19/Sep/18 $$\int\:\frac{\mathrm{1}}{\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{2}}} \:+\:\:\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}} }\:\:\:\mathrm{dx} \\ $$ Answered by Joel578 last updated on 19/Sep/18 $${u}\:=\:\:{x}^{\frac{\mathrm{1}}{\mathrm{6}}} \:\:\rightarrow\:\:{u}^{\mathrm{6}} \:=\:{x} \\…