Question Number 123255 by mnjuly1970 last updated on 24/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\ast\ast\ast\:\:{nice}\:\:{calculus}\:\ast\ast\ast \\ $$$$\:\:\:\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\Phi=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {log}^{\mathrm{3}} \left({tan}\left({x}\right)\right){dx}\:=? \\ $$ Answered by Dwaipayan Shikari last updated…
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Question Number 123234 by benjo_mathlover last updated on 24/Nov/20 $$\:\:\int\:\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}}\:{dx}\: \\ $$ Commented by liberty last updated on 24/Nov/20 Answered by MJS_new last updated…
Question Number 57667 by maxmathsup by imad last updated on 09/Apr/19 $${calculate}\:{U}_{{n}} =\int_{\frac{\pi}{{n}}} ^{\frac{\mathrm{2}\pi}{{n}}} \:\:\:\:\:\frac{{dx}}{\mathrm{2}\:+{sinx}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:\:\:\:\:\:\:{and}\:{lim}_{{n}\rightarrow+\infty} \:\:{nU}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:\Sigma\:{U}_{{n}} \\ $$ Commented by…
Question Number 57668 by maxmathsup by imad last updated on 09/Apr/19 $${let}\:{V}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}+\frac{\mathrm{1}}{{n}}} \:\:\:\:\frac{{x}+\mathrm{1}}{\:\sqrt{\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{3}}}\:{dx}\:\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:{V}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma\:{V}_{{n}} \\ $$ Commented by…
Question Number 57666 by maxmathsup by imad last updated on 09/Apr/19 $$\left.\mathrm{1}\right)\:{calculate}\:{f}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{t}^{\mathrm{2}} \:+\mathrm{2}{sin}\theta{t}\:+\mathrm{1}}{dt}\:\:\:\:{with}\:\mathrm{0}\leqslant\theta\leqslant\frac{\pi}{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({t}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{t}^{\mathrm{2}} \:+\mathrm{2}\left({sin}\theta\right){t}\:+\mathrm{1}}{d}\theta \\ $$$$\left.\mathrm{3}\right)\:{find}\:{also}\:{h}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{t}}{\:\sqrt{{t}^{\mathrm{2}} \:+\mathrm{2}\left({sin}\theta\right){t}\:+\mathrm{1}}}{dt}…
Question Number 57665 by maxmathsup by imad last updated on 09/Apr/19 $${let}\:{f}\left({a}\right)\:=\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \sqrt{{a}+{tan}^{\mathrm{2}} {x}}{dx}\:\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:\:{find}\:{also}\:{g}\left({a}\right)\:=\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\:\frac{{dx}}{\:\sqrt{{a}+{tan}^{\mathrm{2}} {x}}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{values}\:{of}\:\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}}…
Question Number 57653 by MJS last updated on 09/Apr/19 $$\mathrm{is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{value}\:\mathrm{of}\:{I}? \\ $$$${I}=\underset{\mathrm{0}} {\overset{\pi} {\int}}\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)\:{dx} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 09/Apr/19 Commented by…
Question Number 123177 by shree last updated on 23/Nov/20 $${lebesgue}\:{measure}\:{on}\:\left[\mathrm{0}\:\mathrm{1}\right]\:{is}\:{finite}\:?\:{true}\:{or}\:{false}\:{give}\:{reason} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 123159 by Lordose last updated on 23/Nov/20 $$\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \mathrm{log}^{\mathrm{2}} \left(\mathrm{tan}\left(\mathrm{x}\right)\right)\mathrm{dx} \\ $$ Answered by mnjuly1970 last updated on 23/Nov/20 $${ans}:=\frac{\pi^{\mathrm{3}} }{\mathrm{8}} \\…