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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}…