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Category: Integration

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} \\…

sin-x-dx-

Question Number 43981 by Necxx last updated on 19/Sep/18 $$\int\sqrt{\mathrm{sin}\:{x}}\:{dx} \\ $$ Commented by MJS last updated on 19/Sep/18 $$\mathrm{see}\:\mathrm{question}\:\mathrm{42945} \\ $$$$\mathrm{you}'\mathrm{ll}\:\mathrm{have}\:\mathrm{to}\:\mathrm{scroll}\:\mathrm{down}\:\mathrm{a}\:\mathrm{while},\:\mathrm{Sir}\:\mathrm{Tanmay} \\ $$$$\mathrm{has}\:\mathrm{found}\:\mathrm{a}\:\mathrm{way}\:\mathrm{and}\:\mathrm{I}\:\mathrm{also}\:\mathrm{added}\:\mathrm{some}\:\mathrm{useful} \\…