integral of integral of e^{-(9x^2+y^2)}

Lösung

\int \int e^{- (9 x^{2} + y^{2})} d A

C x + \frac{π}{6} A e^{- y^{2}} erf (9 x) + C

Schritte zur Lösung

\int \int e^{- (9 x^{2} + y^{2})} d A

\int e^{- (9 x^{2} + y^{2})} d A = e^{- y^{2} - 9 x^{2}} A + C

= \int (e^{- y^{2} - 9 x^{2}} A + C)

\int (e^{- y^{2} - 9 x^{2}} A + C) d x = C x + \frac{π}{6} A e^{- y^{2}} erf (9 x) + C

= C x + \frac{π}{6} A e^{- y^{2}} erf (9 x) + C

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