What is the integral of e^{-x^2-y^2} ?

The integral of e^{-x^2-y^2} is e^{-y^2}(sqrt(pi))/2 \erf(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{-x^2-y^2}

\int e^{- x^{2} - y^{2}}

e^{- y^{2}} \frac{π}{2} erf (x) + C

Solution steps

\int e^{- x^{2} - y^{2}} d x

Simplify

e^{- y^{2} - x^{2}} : e^{- y^{2}} e^{- x^{2}}

= \int e^{- y^{2}} e^{- x^{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{- y^{2}} \cdot \int e^{- x^{2}} d x

Use the nonelementary integral:

\int e^{- x^{2}} d x = \frac{π}{2} erf (x)

= e^{- y^{2}} \frac{π}{2} erf (x)

Add a constant to the solution

= e^{- y^{2}} \frac{π}{2} erf (x) + C

f (x) = \frac{x}{x ^{2} + 8}

f (x) = e^{x^{3} l n (x)}

\int \frac{9 sin ( x ) + 4 sec ( x )}{tan ( x )} d x

f (x) = \frac{6}{3 x + 1}

f (x) = 8 - 2 x

What is the integral of e^{-x^2-y^2} ?
The integral of e^{-x^2-y^2} is e^{-y^2}(sqrt(pi))/2 \erf(x)+C