Question Number 54033 by qw last updated on 28/Jan/19 $$\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\:{dx}\:= \\ $$ Commented by maxmathsup by imad last updated on 29/Jan/19 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 54032 by qw last updated on 28/Jan/19 $$\underset{−\mathrm{2}\:} {\overset{\mathrm{2}} {\int}}\:\mathrm{min}\:\left({x}−\left[{x}\right],\:−{x}−\left[−{x}\right]\right){dx}\:\mathrm{equals}\:\left[{x}\right] \\ $$$$\mathrm{represents}\:\mathrm{greatest}\:\mathrm{integer}\:\mathrm{less}\:\mathrm{than}\:\mathrm{or} \\ $$$$\left.\mathrm{equal}\:\mathrm{to}\:{x}\right). \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 28/Jan/19…
Question Number 54031 by qw last updated on 28/Jan/19 $$\mathrm{If}\:\:{f}\left({a}+{b}−{x}\right)=\:{f}\left({x}\right),\:\mathrm{then}\:\underset{{a}} {\overset{{b}} {\int}}\:{x}\:{f}\left({x}\right)\:{dx}\:= \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 28/Jan/19 $${I}=\int_{{a}} ^{{b}} {xf}\left({x}\right){dx} \\…
Question Number 54029 by qw last updated on 28/Jan/19 $$\underset{\:\mathrm{3}} {\overset{\mathrm{9}} {\int}}\:\frac{\sqrt{{x}}}{\:\sqrt{\mathrm{12}−{x}}\:+\:\sqrt{{x}}}\:{dx}\:=\:\mathrm{9} \\ $$ Commented by maxmathsup by imad last updated on 29/Jan/19 $$\left.{let}\:{prove}\:{that}\:\int_{{a}} ^{{b}}…
Question Number 54028 by qw last updated on 28/Jan/19 $$\mathrm{If}\:\mathrm{for}\:\mathrm{every}\:\mathrm{integer}\:{n},\:\underset{{n}} {\overset{{n}+\mathrm{1}} {\int}}{f}\left({x}\right)\:{dx}\:=\:{n}^{\mathrm{2}} , \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\underset{−\mathrm{2}} {\overset{\mathrm{4}} {\int}}\:{f}\left({x}\right)\:{dx}= \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…
Question Number 53924 by F_Nongue last updated on 27/Jan/19 $$\mathrm{If}\:\mathrm{the}\:\mathrm{non}−\mathrm{zero}\:\mathrm{numbers}\:{x},\:{y},\:{z}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}, \\ $$$$\mathrm{and}\:\mathrm{tan}^{−\mathrm{1}} {x},\:\mathrm{tan}^{−\mathrm{1}} {y},\:\mathrm{tan}^{−\mathrm{1}} {z}\:\mathrm{are}\:\mathrm{also}\:\mathrm{in}\:\mathrm{AP}, \\ $$$$\mathrm{then} \\ $$ Answered by $@ty@m last updated on…
Question Number 53894 by muhsangsll last updated on 27/Jan/19 $$\underset{\pi/\mathrm{6}} {\overset{\mathrm{5}\pi/\mathrm{6}} {\int}}\sqrt{\mathrm{4}−\mathrm{4}\:\mathrm{sin}^{\mathrm{2}} {t}}\:{dt}\:= \\ $$ Answered by byaw last updated on 27/Jan/19 $$\int_{\pi/\mathrm{6}} ^{\mathrm{5}\pi/\mathrm{6}} \sqrt{\mathrm{4}\left(\mathrm{1}−{sin}^{\mathrm{2}}…
Question Number 53697 by gunawan last updated on 25/Jan/19 $$\mathrm{The}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\underset{\mathrm{log}\:\mathrm{2}} {\overset{{x}} {\int}}\:\:\frac{\mathrm{1}}{\:\sqrt{{e}^{{x}} −\mathrm{1}}}\:{dx}=\:\frac{\pi}{\mathrm{6}}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$ Commented by Abdo msup. last updated on 25/Jan/19…
Question Number 53696 by gunawan last updated on 25/Jan/19 $$\mathrm{Let}\:{I}_{{n}} =\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\mathrm{tan}^{{n}} {x}\:{dx},\:\left({n}>\mathrm{1}\:\mathrm{and}\:{n}\in{N}\right),\:\mathrm{then} \\ $$ Commented by Abdo msup. last updated on 25/Jan/19 $${sir}\:{this}\:{integral}\:{is}\:{solved}\:{see}\:{the}\:{platform}……
Question Number 53694 by gunawan last updated on 25/Jan/19 $$\:\underset{\:\mathrm{0}} {\overset{{r}\:\pi} {\int}}\:\:\mathrm{sin}^{\mathrm{2}{n}} {x}\:{dx}\:= \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 25/Jan/19 $$\int_{\mathrm{0}} ^{\pi} {sinxdx}=\mid−{cosx}\mid_{\mathrm{0}}…