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Question Number 219371 Answers: 0 Comments: 0

Question Number 219370 Answers: 0 Comments: 0

Question Number 219349 Answers: 1 Comments: 0

∫_0 ^( ∞) e^(−r^2 ) cos(r) dr=??

$$\int_{\mathrm{0}} ^{\:\infty} \:{e}^{−{r}^{\mathrm{2}} } \mathrm{cos}\left({r}\right)\:\mathrm{d}{r}=?? \\ $$

Question Number 219348 Answers: 0 Comments: 0

∫_0 ^( ∞) Y_0 (z)e^(−2z) dz=?? Y_ν (z) is Second Bessel Function

$$\int_{\mathrm{0}} ^{\:\infty} \:\:{Y}_{\mathrm{0}} \left({z}\right){e}^{−\mathrm{2}{z}} \mathrm{d}{z}=?? \\ $$$${Y}_{\nu} \left({z}\right)\:\mathrm{is}\:\mathrm{Second}\:\mathrm{Bessel}\:\mathrm{Function} \\ $$

Question Number 219347 Answers: 0 Comments: 0

∫_0 ^( ∞) K_0 (z)e^(−kz) dz=??? K_ν (z) is modified Bessel function

$$\int_{\mathrm{0}} ^{\:\infty} \:{K}_{\mathrm{0}} \left({z}\right){e}^{−{kz}} \mathrm{d}{z}=??? \\ $$$${K}_{\nu} \left({z}\right)\:\mathrm{is}\:\mathrm{modified}\:\mathrm{Bessel}\:\mathrm{function} \\ $$

Question Number 219346 Answers: 0 Comments: 0

∫_0 ^( ∞) ln(z)e^(−3z) dz=???

$$\int_{\mathrm{0}} ^{\:\infty} \mathrm{ln}\left({z}\right){e}^{−\mathrm{3}{z}} \mathrm{d}{z}=??? \\ $$

Question Number 219345 Answers: 0 Comments: 0

∫_(−∞) ^(+∞) ∫_(−∞) ^( +∞) −(x/( (√(x^2 +y^2 )))) da=???

$$\int_{−\infty} ^{+\infty} \int_{−\infty} ^{\:+\infty} \:\:−\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }}\:\mathrm{da}=???\:\: \\ $$

Question Number 219344 Answers: 0 Comments: 0

∫_0 ^( ∞) ((cos(z))/( (√(z^2 +1)))) dz=??

$$\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{cos}\left({z}\right)}{\:\sqrt{{z}^{\mathrm{2}} +\mathrm{1}}}\:\mathrm{d}{z}=?? \\ $$

Question Number 219343 Answers: 0 Comments: 0

∫∫∫_( S) e^(−x^2 −y^2 −z^2 ) dA=???

$$\int\int\int_{\:\mathrm{S}} \:{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} −{z}^{\mathrm{2}} } \:\mathrm{dA}=??? \\ $$

Question Number 219365 Answers: 0 Comments: 0

Question Number 219361 Answers: 1 Comments: 0

∫_(−∞) ^(+∞) ((cos(z)e^(−z) )/(z^2 +1)) dz=??

$$\int_{−\infty} ^{+\infty} \:\:\frac{\mathrm{cos}\left({z}\right){e}^{−{z}} }{{z}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{d}{z}=?? \\ $$

Question Number 219360 Answers: 0 Comments: 0

prove Σ_(k=−∞) ^( ∞) J_k (z)=1

$$\mathrm{prove}\:\underset{{k}=−\infty} {\overset{\:\infty} {\sum}}\:{J}_{{k}} \left({z}\right)=\mathrm{1} \\ $$

Question Number 219359 Answers: 0 Comments: 0

is Σ_(k=−∞) ^∞ J_ν (k)= Σ_(k=−∞) ^∞ Σ_(l=0) ^∞ (((−1)^l )/(l!(l+ν)!))((k/2))^(2l+ν) =Σ_(l=0) ^∞ Σ_(k=−∞) ^∞ (((−1)^l )/(l!(l+ν)!))((k/2))^(2l+k) ??

$$\mathrm{is}\:\underset{{k}=−\infty} {\overset{\infty} {\sum}}\:{J}_{\nu} \left({k}\right)= \\ $$$$\underset{{k}=−\infty} {\overset{\infty} {\sum}}\:\underset{{l}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{l}} }{{l}!\left({l}+\nu\right)!}\left(\frac{{k}}{\mathrm{2}}\right)^{\mathrm{2}{l}+\nu} =\underset{{l}=\mathrm{0}} {\overset{\infty} {\sum}}\:\underset{{k}=−\infty} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{l}} }{{l}!\left({l}+\nu\right)!}\left(\frac{{k}}{\mathrm{2}}\right)^{\mathrm{2}{l}+{k}} ?? \\ $$

Question Number 219358 Answers: 0 Comments: 0

Σ_(h=−∞) ^∞ J_ν (h)=?? , ν∈Z\{2Z}

$$\underset{{h}=−\infty} {\overset{\infty} {\sum}}{J}_{\nu} \left({h}\right)=??\:,\:\nu\in\mathbb{Z}\backslash\left\{\mathrm{2}\mathbb{Z}\right\} \\ $$

Question Number 219357 Answers: 1 Comments: 0

∫_0 ^( ∞) ((ln(z))/(z^2 +1)) dz

$$\int_{\mathrm{0}} ^{\:\infty} \:\:\:\frac{\mathrm{ln}\left({z}\right)}{{z}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{d}{z} \\ $$

Question Number 219356 Answers: 1 Comments: 0

∫_0 ^( ∞) ((1−cos^2 (z))/z^2 )e^(−zt) dz

$$\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{\mathrm{1}−\mathrm{cos}^{\mathrm{2}} \left({z}\right)}{{z}^{\mathrm{2}} }{e}^{−{zt}} \:\mathrm{d}{z} \\ $$

Question Number 219355 Answers: 1 Comments: 0

∫_0 ^( ∞) ((sin(z))/z)e^(−zt) dz=??

$$\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{\mathrm{sin}\left({z}\right)}{{z}}{e}^{−{zt}} \mathrm{d}{z}=?? \\ $$

Question Number 219354 Answers: 1 Comments: 0

∫_(−∞) ^( +∞) ze^(−z^3 ) dz=??

$$\int_{−\infty} ^{\:+\infty} \:\:{ze}^{−{z}^{\mathrm{3}} } \:\mathrm{d}{z}=?? \\ $$

Question Number 219352 Answers: 1 Comments: 0

Question Number 219351 Answers: 1 Comments: 0

Question Number 219350 Answers: 1 Comments: 0

∫ (1/(cos(u)+sin(u)+1)) du=??

$$\int\:\:\frac{\mathrm{1}}{\mathrm{cos}\left({u}\right)+\mathrm{sin}\left({u}\right)+\mathrm{1}}\:\mathrm{d}{u}=?? \\ $$

Question Number 219341 Answers: 1 Comments: 1

∫(dx/(1 + sin^3 x + cos^3 x))

$$\int\frac{{dx}}{\mathrm{1}\:+\:{sin}^{\mathrm{3}} {x}\:+\:{cos}^{\mathrm{3}} {x}} \\ $$

Question Number 219340 Answers: 1 Comments: 0

F^→ (x,y,z)=−(x/( (√(x^2 +y^2 +z^2 ))))e_1 ^→ −(y/( (√(x^2 +y^2 +z^2 ))))e_2 ^→ −(z/( (√(x^2 +y^2 +z^2 ))))e_3 ^→ x^2 +y^2 +z^2 =R^2 ∫∫_( S) F^→ ∙dS^→ =??

$$\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\left({x},{y},{z}\right)=−\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} }}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} −\frac{{y}}{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} }}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} −\frac{{z}}{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} }}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{3}} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} ={R}^{\mathrm{2}} \\ $$$$\int\int_{\:\boldsymbol{\mathcal{S}}} \:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\centerdot\mathrm{d}\overset{\rightarrow} {\boldsymbol{\mathcal{S}}}=?? \\ $$

Question Number 219339 Answers: 4 Comments: 0

Question Number 219338 Answers: 0 Comments: 0

F^→ =−xe_1 ^→ −ye_2 ^→ −ze_3 ^→ S^→ (u,v)= { (((2+3sin(u))cos(v))),(((2+3sin(v))sin(u))),((3cos(u))) :} u∈[0,2π] , v∈[0,2π] ∫∫_( S) F^→ ∙dS^→ =???

$$\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}=−{x}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} −{y}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} −{z}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{3}} \\ $$$$\overset{\rightarrow} {\boldsymbol{\mathcal{S}}}\left({u},{v}\right)=\begin{cases}{\left(\mathrm{2}+\mathrm{3sin}\left({u}\right)\right)\mathrm{cos}\left({v}\right)}\\{\left(\mathrm{2}+\mathrm{3sin}\left({v}\right)\right)\mathrm{sin}\left({u}\right)}\\{\mathrm{3cos}\left({u}\right)}\end{cases} \\ $$$${u}\in\left[\mathrm{0},\mathrm{2}\pi\right]\:,\:{v}\in\left[\mathrm{0},\mathrm{2}\pi\right] \\ $$$$\int\int_{\:\boldsymbol{\mathcal{S}}} \:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\centerdot\mathrm{d}\overset{\rightarrow} {\boldsymbol{\mathcal{S}}}=??? \\ $$

Question Number 219337 Answers: 5 Comments: 0

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