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advnced-calculus-prove-0-sin-tan-x-x-dx-pi-2-1-1-e-prove-that-0-1-e-x-2-x-2-dx-pi-

Question Number 133490 by mnjuly1970 last updated on 22/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….\:{advnced}\:\:{calculus}…. \\ $$$$\:\:\:\:{prove}:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({tan}\left({x}\right)\right)}{{x}}{dx}=\frac{\pi}{\mathrm{2}}\left(\mathrm{1}−\frac{\mathrm{1}}{{e}}\right) \\ $$$$\:{prove}\:{that}:\:\boldsymbol{\Phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}−{e}^{−{x}^{\mathrm{2}} } }{{x}^{\mathrm{2}} }{dx}=\sqrt{\pi} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:…

Question-133487

Question Number 133487 by mr W last updated on 22/Feb/21 Commented by mr W last updated on 22/Feb/21 $${a}\:{ball}\:{is}\:{projected}\:{along}\:{the}\:{smooth} \\ $$$${floor}\:{and}\:{returns}\:{back}\:{after}\:{two} \\ $$$${times}\:{impact}\:{with}\:{the}\:{circular}\:{wall}. \\ $$$${if}\:{the}\:{restitution}\:{coefficient}\:{is}\:{e},…

use-Green-Riemann-formuler-to-determined-I-D-xydxdy-D-x-y-R-2-x-0-y-x-y-1-

Question Number 67946 by Cmr 237 last updated on 02/Sep/19 $$\mathrm{use}\:\boldsymbol{\mathrm{Green}}−\boldsymbol{\mathrm{Riemann}}\:\boldsymbol{\mathrm{formuler}} \\ $$$$\mathrm{to}\:\mathrm{determined}: \\ $$$$\boldsymbol{\mathrm{I}}=\int\int_{\boldsymbol{\mathrm{D}}} \boldsymbol{\mathrm{xy}}\mathrm{dxdy} \\ $$$$\boldsymbol{\mathrm{D}}=\left\{\left(\mathrm{x},\mathrm{y}\right)\in\mathbb{R}^{\mathrm{2}} \mid\mathrm{x}\geqslant\mathrm{0};\mathrm{y}\geqslant;\mathrm{x}+{y}\leqslant\mathrm{1}\right\} \\ $$ Commented by mathmax by…

we-consider-that-application-n-1-det-M-n-R-R-A-det-A-1-verify-that-H-M-n-R-and-t-R-if-A-I-n-det-A-tH-1-t-Tr-H-t-2-suppose-that-A-GL-n-R-prouve-that-the-d

Question Number 133482 by AbderrahimMaths last updated on 22/Feb/21 $$\:\:\:\:{we}\:{consider}\:{that}\:{application}\:{n}\geqslant\mathrm{1} \\ $$$$\:\:{det}\::\:{M}_{{n}} \left(\mathbb{R}\right)\rightarrow\mathbb{R} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{A} {det}\left({A}\right) \\ $$$$\mathrm{1}−{verify}\:{that}\:\forall{H}\in{M}_{{n}} \left(\mathbb{R}\right)\:{and}\:{t}\in\mathbb{R} \\ $$$$\:{if}\:{A}={I}_{{n}} \Rightarrow{det}\left({A}+{tH}\right)=\mathrm{1}+{t}.{Tr}\left({H}\right)+\circ\left({t}\right) \\ $$$$\mathrm{2}−{suppose}\:{that}:\:{A}\in{GL}_{{n}} \left(\mathbb{R}\right)…

e-y-2-2-dy-

Question Number 67942 by mhmd last updated on 02/Sep/19 $$\int{e}^{{y}^{\mathrm{2}} /\mathrm{2}} \:\:{dy} \\ $$ Commented by mr W last updated on 09/Feb/21 $$\int{e}^{\frac{{y}^{\mathrm{2}} }{\mathrm{2}}} {dy}=\sqrt{\frac{\pi}{\mathrm{2}}}\:{erfi}\left(\frac{{y}}{\:\sqrt{\mathrm{2}}}\right)+{C}…