Question Number 215414 by MATHEMATICSAM last updated on 06/Jan/25 $$\int\:\frac{\mathrm{sin}^{\mathrm{3}} \left(\frac{{x}}{\mathrm{2}}\right)\mathrm{sec}\left(\frac{{x}}{\mathrm{2}}\right)}{\:\sqrt{\mathrm{cos}^{\mathrm{3}} {x}\:+\:\mathrm{cos}^{\mathrm{2}} {x}\:+\:\mathrm{cos}{x}}}\:{dx} \\ $$$$\mathrm{Solve}\:\mathrm{this}\:\mathrm{integral}. \\ $$ Commented by JamesZhou last updated on 06/Jan/25 $${maybe}\:{numerator}\:{issi}\hat…
Question Number 215434 by ajfour last updated on 06/Jan/25 $$\int_{\mathrm{0}} ^{\:\:{t}} \sqrt{\frac{{t}}{{b}−{t}}}\:{e}^{{t}} {dt}\:=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 215404 by ajfour last updated on 05/Jan/25 $$\int_{{a}} ^{\:\:{x}} \:\frac{\sqrt{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} }}{\:\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }}{dx}\:=\:? \\ $$ Answered by Ghisom last updated on 06/Jan/25 $$\int\frac{\sqrt{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}}…
Question Number 215390 by MathematicalUser2357 last updated on 05/Jan/25 $$\oint_{\gamma} {x}^{\mathrm{2}} {dx}\:\left[\gamma:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1}\right] \\ $$ Answered by MrGaster last updated on 05/Jan/25 $$\mathrm{solve}:\int_{\mathrm{0}} ^{\mathrm{2}\pi}…
Question Number 215393 by MrGaster last updated on 05/Jan/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{2}\nu} }{\left({x}^{\mathrm{2}} +\beta^{\mathrm{2}} \right)^{\mu+\mathrm{1}} }\mathrm{sin}\left({ax}\right){dx} \\ $$$$ \\ $$ Commented by JamesZhou…
Question Number 215410 by York12 last updated on 05/Jan/25 $$\mathrm{The}\:\mathrm{following}\:\mathrm{diagram}\:\mathrm{shows}\:\mathrm{the}\:\mathrm{relationship} \\ $$$$\mathrm{between}\:\mathrm{electromotive}\:\mathrm{force}\:\left(\mathrm{e}.\mathrm{m}.\mathrm{f}\right)\:\mathrm{and}\:\mathrm{the}\:\mathrm{time}\:\left(\mathrm{t}\right)\:\mathrm{in}\:\mathrm{a}\:\mathrm{dynamo} \\ $$$$\mathrm{coil}.\mathrm{During}\:\mathrm{the}\:\mathrm{time}\:\mathrm{interval}\:\mathrm{from}\:\mathrm{t}=\mathrm{0}\:\mathrm{to}\:\mathrm{t}=\frac{\mathrm{1}}{\mathrm{30}}\:\mathrm{seconds},\: \\ $$$$\mathrm{the}\:\mathrm{average}\:\mathrm{electromotive}\:\mathrm{force}\:\left(\mathrm{e}.\mathrm{m}.\mathrm{f}\right)\:\mathrm{induced}\:\mathrm{in}\:\mathrm{the}\:\mathrm{coil}\:\mathrm{is}: \\ $$$$\left(\mathrm{a}\right)\mathrm{42}.\mathrm{46}\:{V} \\ $$$$\left(\mathrm{b}\right)\mathrm{19}.\mathrm{11}\:{V} \\ $$$$\left(\mathrm{c}\right)\mathrm{127}.\mathrm{39}\:{V} \\ $$$$\left(\mathrm{d}\right)\mathrm{173}.\mathrm{21}\:{V} \\…
Question Number 215386 by JasonHidd last updated on 04/Jan/25 Answered by mr W last updated on 04/Jan/25 $$\int_{\mathrm{0}} ^{{x}} {f}\left({x}\right){dx}=\underset{\mathrm{0}} {\int}^{−{x}} {f}\left({x}\right){dx}+\int_{−{x}} ^{{x}} {f}\left({x}\right){dx} \\…
Question Number 215344 by universe last updated on 03/Jan/25 Answered by MrGaster last updated on 04/Jan/25 $$\:\mathrm{Let}\:\Sigma\:\mathrm{be}\:\mathrm{the}\:\mathrm{boundary}\:\mathrm{of}\:{D}. \\ $$$$\Sigma=\sum_{\mathrm{1}} \cup\sum_{\mathrm{2}} \cup\sum_{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{where} \\ $$$$\sum_{\mathrm{1}}…
Question Number 215280 by universe last updated on 02/Jan/25 $${volume}\:{of}\:{solids}\:{generated}\:{by}\:{revolving} \\ $$$${the}\:{region}\:{bounded}\:{by}\:{the}\:{curve}\:{and}\:{line} \\ $$$$\:{the}\:{y}-{axis} \\ $$$$\:{y}={x}\:,{y}\:=\:{x}/\mathrm{2}\:,{x}\:=\:\mathrm{2} \\ $$ Commented by mr W last updated on…
Question Number 215315 by depressiveshrek last updated on 02/Jan/25 $$\mathrm{Evaluate}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{2}}+…+\frac{\mathrm{1}}{\mathrm{4}{n}}\right) \\ $$ Answered by mr W last updated on 02/Jan/25 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{k}=\mathrm{1}} {\overset{\mathrm{2}{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{2}{n}+{k}}…