Rozwiąż I _ { 1 } = ∫ (from 0 to infty) of int_0^inftye^-x^2e^-4^2 wrt xdy

Rozwiąż względem I_1

I_{1}=\int _{0}^{\infty}\int _{0}^{\infty}e^{-x^{2}-16}\mathrm{d}x\mathrm{d}y

Przypisz I_1

I_{1}≔\int _{0}^{\infty}\int _{0}^{\infty}e^{-x^{2}-16}\mathrm{d}x\mathrm{d}y

Quiz

Integration

I _ { 1 } = \int _ { 0 } ^ { \infty } \int _ { 0 } ^ { \infty } e ^ { - x ^ { 2 } } e ^ { - 4 ^ { 2 } } d x d y

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https://math.stackexchange.com/questions/2016227/evaluating-the-improper-integral-int-0-infty-int-0-infty-e-2x7y-matho

Hint: this problem actually reduces to calculating \left(\int_0^{\infty}e^{-2x}\,dx\right)\cdot\left(\int_0^{\infty}e^{-7y}\,dy\right) Why?

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https://math.stackexchange.com/questions/2622068/how-to-calculate-iint-mathbbr2-exp-left-x2-y2ixy-ix-iy-right-dx

This is a Gaussian double-integral I ~:=~\iint_{\mathbb{R}^2} \! dx~dy~ e^{-S(x,y)} ,\tag{1} where S(x,y)~:=~x^2+y^2-ixy+ix+iy. \tag{2} One method is to change coordinates x^{\pm}=\frac{x\pm y}{\sqrt{2}} ...

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https://math.stackexchange.com/q/2662355

Observe that we can factor the joint density as f(x,y)=e^{-\lambda x}e^{-\lambda y}; \quad (x,y\geq 0)\tag{1}. Let I=\int_0^\infty\int_0^\infty f(x,y)\,dx\,dy and note that I=\int_0^\infty\int_0^\infty e^{-\lambda x}e^{-\lambda y}\, dx \,dy =\int_0^\infty e^{-\lambda y}\left[\int_0^\infty e^{-\lambda x}\, dx \right]\,dy =\left[\int_0^\infty e^{-\lambda x}\, dx \right]\left[\int_0^\infty e^{-\lambda y}\, dy \right] ...

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https://www.quora.com/How-do-I-solve-this-integration-int_-0-infty-int_-0-infty-x-y-e-ax-e-by-dxdy

Split the integration domain into two separate domains: one with x>y and one with x<y. x>y : \int_0^\infty \int_y^\infty (x-y) e^{-ax} dx \,e^{-by} dy and x<y : \int_0^\infty \int_0^y (y-x) e^{-ax} dx \,e^{-by} dy ...

Need help understanding why \int_0^\infty \int_0^\infty |x-y|e^{-x}e^{-y} \, dx \,dy = 2 \int_0^\infty \int_y^\infty (x-y)e^{-x}e^{-y} \, dx \,dy

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Note that \tag{*} \int_0^\infty\int_0^\infty |x-y|e^{-x}e^{-y} \, dx\, dy \\ = \int_0^\infty\int_y^\infty (x-y)e^{-x}e^{-y} \, dx\, dy + \int_0^\infty\int_0^y (y-x)e^{-x}e^{-y} \, dx\, dy The ...

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Przykłady

Równanie kwadratowe

{ x } ^ { 2 } - 4 x - 5 = 0

Trygonometria

4 \sin \theta \cos \theta = 2 \sin \theta

\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]

Równania równoważne

\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.

Różniczkowanie

\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }

Całkowanie

\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x

Granice

\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}

Tematy

Tematy

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