Question Number 72888 by mathmax by abdo last updated on 04/Nov/19 $${let}\:{f}\left({x}\right)=\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{tant}}{\mathrm{2}+{x}\:{cost}}{dt}\:\:{with}\:{x}\:{real} \\ $$$$\left.\mathrm{1}\right){determine}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){determine}\:{also}\:{g}\left({x}\right)=\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{tant}}{\left(\mathrm{2}+{xcost}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{tant}}{\left(\mathrm{2}+\mathrm{3}{cost}\right)}{dt}\:{and}\:\int_{\frac{\pi}{\mathrm{6}}}…
Question Number 72889 by mathmax by abdo last updated on 04/Nov/19 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right){n}^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 72886 by mhmd last updated on 04/Nov/19 $${let}\:{w}={f}\left({x},\:{y}\right)\:{be}\:{a}\:{differentiable}\:{function}\:{where}\:{x}={rcos}\theta\:{and}\:{y}={rsin}\theta\:{show}\:{that}\:\left({f}_{{x}} \right)^{\mathrm{2}} +\left({f}_{{y}} \right)^{\mathrm{2}} =\left({w}_{{x}} \right)^{\mathrm{2}} +\mathrm{1}/{r}^{\mathrm{2}} \left({w}_{{y}} \right)^{\mathrm{2}} ? \\ $$$${help}\:{me}\:{sir}\: \\ $$ Answered by…
Question Number 72884 by mhmd last updated on 04/Nov/19 $${find}\:{the}\:{area}\:{of}\:{the}\:{region}\:{bounded}\:{by}\:{the}\:{semicircle}\:{y}=\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }\:{and}\:{the}\:{x}=+−{a}\:\:{and}\:{the}\:{line}\:{y}=−{a}\:?\:{by}\:{using}\:{intigiral} \\ $$$${pleas}\:{sir}\:{help}\:{me} \\ $$ Commented by kaivan.ahmadi last updated on 04/Nov/19 $$\int_{−{a}} ^{{a}}…
Question Number 138422 by mnjuly1970 last updated on 13/Apr/21 $$\:\:\:\:\:\:\:\:\:…….{nice}\:\:\:\:\:{calculus}….. \\ $$$$\:\:\:{evaluate}: \\ $$$$\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \:\frac{\sqrt[{\mathrm{3}}]{\mathrm{1}+{x}}\:−\sqrt[{\mathrm{3}}]{{x}}}{\:\sqrt{{x}}}\:^{\:\:} {dx}=? \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 138417 by bemath last updated on 13/Apr/21 $$ \\ $$the x axis is transformed with respect to the line y = 2x +2,…
Question Number 72883 by mhmd last updated on 04/Nov/19 $${if}\:{w}={f}\left({u}\:{and}\:{v}\right)\:{where}\:{f}_{{uu}} +{f}_{{vv}} =\mathrm{0}\:{and}\:{u}=\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)/\mathrm{2}\:{and}\:{v}={xy}\:{show}\:{that}\:{w}_{{xx}} +{w}_{{yy}} =\mathrm{0}\:? \\ $$$${pleas}\:{sir}\:{help}\:{me} \\ $$ Answered by mind is power…
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Question Number 138415 by tugu last updated on 13/Apr/21 $${A},{B}\:\in{R},\:\:{f}\left(\mathrm{1}\right)=\mathrm{0}\:,\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\left({f}\left({x}\right)\right)^{\mathrm{2}} {dx}\:={A}\:{and}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{xf}\left({x}\right){dx}={B}\: \\ $$$${what}\:{is}\:{the}\:{integral}\:{value}\:{of}\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{xf}\left({x}\right)\left({f}\:'\left({x}\right)−\mathrm{1}\right){dx}\:{by}\:{using}\:{trrms}\:{of}\:{A}\:{and}\:{B}\:?\: \\ $$ Answered by Ar Brandon…