integral from 0 to 1 of integral from 0 to 2 of xye^{xy^2}

Lösung

\int_{0}^{1} \int_{0}^{2} x y e^{x y^{2}} d x d y

\frac{e ^{2} - 1}{2} - 1

Dezimale

2.19452 \dots

Schritte zur Lösung

\int_{0}^{1} \int_{0}^{2} x y e^{x y^{2}} d x d y

\int_{0}^{2} x y e^{x y^{2}} d x = \frac{2 y ^{2} e ^{2 y^{2}} - e ^{2 y^{2}} + 1}{y ^{3}}

= \int_{0}^{1} (\frac{2 y ^{2} e ^{2 y^{2}} - e ^{2 y^{2}} + 1}{y ^{3}}) d y

\int_{0}^{1} (\frac{2 y ^{2} e ^{2 y^{2}} - e ^{2 y^{2}} + 1}{y ^{3}}) d y = \frac{e ^{2} - 1}{2} - 1

= \frac{e ^{2} - 1}{2} - 1

\int (e^{2 x} + 4)^{- 1} d x

\int_{l n (4)}^{l n (25)} e^{\frac{x}{2}} d x

x \to 0 lim (- \frac{5}{1 - 5 x})

\frac{d y}{d x} = \frac{1}{1 - x}, y (0) = 1

d er i v a t i v e f (x) = \frac{x ^{2} + 2 x - 4}{( x + 1 ) ^{2}}