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Category: Integration

a-b-x-a-b-x-dx-

Question Number 87757 by john santu last updated on 06/Apr/20 $$\int_{\mathrm{a}} ^{\mathrm{b}} \:\frac{\sqrt{\mathrm{x}−\mathrm{a}}}{\:\sqrt{\mathrm{b}−\mathrm{x}}}\:\mathrm{dx}\:=?\: \\ $$ Commented by john santu last updated on 06/Apr/20 $$\left.\mathrm{let}\:\mathrm{x}\:=\:\mathrm{a}\:+\:\left(\mathrm{b}−\mathrm{a}\right)\:\mathrm{w}\:\right] \\…

4x-e-3x-dx-

Question Number 22210 by cmaxamuud98 @gmail.com last updated on 13/Oct/17 $$\int\frac{\mathrm{4}{x}}{{e}^{\mathrm{3}{x}} }{dx} \\ $$ Answered by ajfour last updated on 13/Oct/17 $$=\mathrm{4}\int{xe}^{−\mathrm{3}{x}} {dx} \\ $$$$=\mathrm{4}\left\{{x}\int{e}^{−\mathrm{3}{x}}…

Question-87716

Question Number 87716 by Power last updated on 05/Apr/20 Commented by malwaan last updated on 05/Apr/20 $${put}\:{x}=\mathrm{2}{sin}\:{y}\:\Rightarrow\:{dx}=\mathrm{2}{cosydy} \\ $$$$\mathrm{3}{x}−{x}^{\mathrm{3}} \:=\:\mathrm{2}{sin}\mathrm{3}{y} \\ $$$$\therefore\:\int\:^{\mathrm{3}} \sqrt{\mathrm{2}{sin}\mathrm{3}{y}}\:.\:\mathrm{2}{cosy}\:{dy}\:=\:?? \\ $$…

If-1-4-f-x-dx-5-what-is-the-value-of-0-1-f-3x-1-dx-

Question Number 22166 by Joel577 last updated on 12/Oct/17 $$\mathrm{If}\underset{\mathrm{1}} {\overset{\mathrm{4}} {\int}}\:{f}\left({x}\right)\:{dx}\:=\:\mathrm{5} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{f}\left(\mathrm{3}{x}\:+\mathrm{1}\right)\:{dx}\:? \\ $$ Answered by ajfour last updated on 12/Oct/17…