Question Number 27294 by iy last updated on 04/Jan/18 $$\underset{\mathrm{1}/{e}} {\overset{\mathrm{tan}\:{x}} {\int}}\frac{{t}}{\mathrm{1}+{t}^{\mathrm{2}} }\:{dt}\:+\:\underset{\mathrm{1}/{e}} {\overset{\mathrm{cot}\:{x}} {\int}}\:\frac{\mathrm{1}}{{t}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}\:{dt}\:= \\ $$ Commented by prakash jain last updated on…
Question Number 27281 by kemhoney78@gmail.com last updated on 04/Jan/18 $$\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\:\left({x}^{\mathrm{2}} +\mathrm{cos}\:{x}\right)\:\mathrm{log}\:\left(\frac{\mathrm{2}+{x}}{\mathrm{2}−{x}}\right){dx}\:=\:\mathrm{0} \\ $$ Commented by abdo imad last updated on 04/Jan/18 $${let}\:{put}\:\:{f}\left({x}\right)=\:\left({x}^{\mathrm{2}} +{cosx}\right){ln}\left(\frac{\mathrm{2}+{x}}{\left.\mathrm{2}−{x}\right)}\right)\:{we}\:{have}…
Question Number 27280 by kemhoney78@gmail.com last updated on 04/Jan/18 $$\mathrm{If}\:\mathrm{for}\:\mathrm{a}\:\mathrm{real}\:\mathrm{number}\:{y},\:\left[{y}\right]\:\mathrm{is}\:\mathrm{the}\:\mathrm{greatest} \\ $$$$\mathrm{integer}\:\mathrm{less}\:\mathrm{than}\:\mathrm{or}\:\mathrm{equal}\:\mathrm{to}\:{y},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integeral}\:\underset{\pi/\mathrm{2}} {\overset{\mathrm{3}\pi/\mathrm{2}} {\int}}\left[\mathrm{2}\:\mathrm{sin}\:{x}\right]{dx}\:\mathrm{is} \\ $$ Commented by abdo imad last updated on…
Question Number 27258 by hasie09 last updated on 04/Jan/18 $$\mathrm{If}\:\:\mathrm{9}^{{x}} −\mathrm{4}×\mathrm{3}^{{x}+\mathrm{2}} +\mathrm{3}^{\mathrm{5}} =\mathrm{0},\:\mathrm{then}\:\mathrm{the}\:\mathrm{solution} \\ $$$$\mathrm{set}\:\mathrm{is} \\ $$ Commented by tawa tawa last updated on 04/Jan/18…
Question Number 27203 by julli deswal last updated on 03/Jan/18 $$\mathrm{Let}\:{S}\:\subset\:\left(\mathrm{0},\:\pi\right)\:\mathrm{denote}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:{x} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{8}^{\mathrm{1}+\mid\mathrm{cos}\:{x}\mid+\mathrm{cos}^{\mathrm{2}} {x}+\mid\mathrm{cos}^{\mathrm{3}} {x}\mid+…\:\mathrm{to}\:\infty} =\:\mathrm{4}^{\mathrm{3}} \\ $$$$\mathrm{then}\:{S}\:=\: \\ $$ Answered by Tinkutara…
Question Number 92486 by Rohit@Thakur last updated on 07/May/20 $$\mathrm{The}\:\mathrm{smallest}\:\mathrm{interval}\:\left[{a},\:{b}\right]\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }}\:{dx}\:\in\:\left[{a},\:{b}\right]\:\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 26888 by Roshan last updated on 31/Dec/17 $$\mathrm{If}\:\alpha,\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{equation}\: \\ $$$$\mathrm{whose}\:\mathrm{roots}\:\mathrm{are}\:\alpha+\beta,\:\:\alpha\beta. \\ $$ Answered by Rasheed.Sindhi last updated on 31/Dec/17 $${ax}^{\mathrm{2}}…
Question Number 26851 by jain50791@gmail.com last updated on 30/Dec/17 $$\mathrm{Two}\:\mathrm{integers}\:{x}\:\mathrm{and}\:{y}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{with} \\ $$$$\mathrm{replacement}\:\mathrm{out}\:\mathrm{of}\:\mathrm{the}\:\mathrm{set}\:\left\{\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},…,\:\mathrm{10}\right\}. \\ $$$$\mathrm{Then}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mid{x}−{y}\mid>\mathrm{5}\:\mathrm{is} \\ $$ Commented by Rasheed.Sindhi last updated on 30/Dec/17 $$\mathrm{Let}\:\mathrm{x}>\mathrm{y} \\…
Question Number 26771 by julli deswal last updated on 29/Dec/17 $$\underset{\:\mathrm{0}} {\overset{\:\:\:\left[{x}\right]} {\int}}\frac{\mathrm{2}^{{x}} }{\mathrm{2}^{\left[{x}\right]} }\:{dx}\:= \\ $$ Commented by prakash jain last updated on 29/Dec/17…
Question Number 26770 by julli deswal last updated on 29/Dec/17 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left({n}\:!\right)^{\mathrm{1}/{n}} }{{n}}\:= \\ $$ Commented by abdo imad last updated on 29/Dec/17 $${n}!\sim\:{n}^{{n}} \:{e}^{−{n}}…