Menu Close

Category: Integration

find-0-2-x-2-x-2-dx-

Question Number 90171 by M±th+et£s last updated on 21/Apr/20 $${find}\:\int_{\mathrm{0}} ^{\mathrm{2}} \left(\lfloor{x}^{\mathrm{2}} \rfloor+\lfloor{x}\rfloor^{\mathrm{2}} \right){dx} \\ $$ Answered by TANMAY PANACEA. last updated on 21/Apr/20 $${is}\:{it}\:{floor}\:{function}\:\left({greatest}\:{integer}\:{function}\mathrm{3}\right.…

0-pi-2-dx-1-tan-x-

Question Number 155686 by john_santu last updated on 03/Oct/21 $$\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{{dx}}{\mathrm{1}+\mathrm{tan}\:{x}}\:=? \\ $$ Answered by peter frank last updated on 03/Oct/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{cos}\:\mathrm{x}}{\mathrm{cos}\:\mathrm{x}+\mathrm{sin}\:\mathrm{x}}\mathrm{dx}…

I-n-t-0-dt-t-1-t-2-t-n-

Question Number 90135 by Ar Brandon last updated on 21/Apr/20 $$\mathrm{I}_{\mathrm{n}} =\int_{\mathrm{t}=\mathrm{0}} ^{+\infty} \frac{\mathrm{dt}}{\left(\mathrm{t}+\mathrm{1}\right)\left(\mathrm{t}+\mathrm{2}\right)…\left(\mathrm{t}+\mathrm{n}\right)} \\ $$ Answered by TANMAY PANACEA. last updated on 21/Apr/20 $${I}=\int\frac{{dt}}{\left({t}+\mathrm{1}\right)\left({t}+\mathrm{2}\right)\left({t}+\mathrm{3}\right)..\left({t}+{n}\right)}…

2-3-u-2u-e-x-2-2pi-u-1-2-x-3x-2-u-du-u-gt-0-

Question Number 90110 by jagoll last updated on 21/Apr/20 $$\underset{\frac{\mathrm{2}}{\mathrm{3}}\mathrm{u}} {\overset{\mathrm{2u}} {\int}}\:\frac{\mathrm{e}^{−\frac{\mathrm{x}}{\mathrm{2}}} }{\mathrm{2}\pi\:\sqrt{\left(\mathrm{u}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\right)\left(\frac{\mathrm{3x}}{\mathrm{2}}−\mathrm{u}\right)}}\:\mathrm{du}\: \\ $$$$\left(\mathrm{u}\:>\:\mathrm{0}\:\right) \\ $$ Commented by MJS last updated on 21/Apr/20 $$\mathrm{dependent}\:\mathrm{borders}\:\mathrm{are}\:\mathrm{not}\:\mathrm{allowed}…

Question-90055

Question Number 90055 by awlia last updated on 21/Apr/20 Commented by jagoll last updated on 21/Apr/20 $$\mathrm{vol}\:=\:\pi\:\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:\left(\mathrm{4x}−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}} \:\mathrm{dx}\: \\ $$$$=\:\pi\:\left\{\:−\frac{\mathrm{x}^{\mathrm{2}} \left(\mathrm{4}−\mathrm{x}\right)^{\mathrm{3}} }{\mathrm{3}}−\frac{\mathrm{x}\left(\mathrm{4}−\mathrm{x}\right)^{\mathrm{4}}…