integral from 0 to 1 of (-10y)/(e^{2y)}

Lösung

\int_{0}^{1} \frac{- 10 y}{e ^{2 y}} d y

- 10 (- \frac{3}{4 e ^{2}} + \frac{1}{4})

Dezimale

- 1.48498 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{- 10 y}{e ^{2 y}} d y

Entferne die Konstante:

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

= - 10 \cdot \int_{0}^{1} \frac{y}{e ^{2 y}} d y

Wende die partielle Integration an

= - 10 [- \frac{1}{2} e^{- 2 y} y - \int - \frac{1}{2} e^{- 2 y} d y]_{0}^{1}

\int - \frac{1}{2} e^{- 2 y} d y = \frac{1}{4} e^{- 2 y}

= - 10 [- \frac{1}{2} e^{- 2 y} y - \frac{1}{4} e^{- 2 y}]_{0}^{1}

Berechne die Grenzen:

- \frac{3}{4 e ^{2}} + \frac{1}{4}

= - 10 (- \frac{3}{4 e ^{2}} + \frac{1}{4})

x \to 0 + lim ((x) (e^{\frac{1}{x}}))

d er i v a t i v e f (x) = 12 x^{2} - 36 x

\frac{d y}{d x} = \frac{( 1 - y )}{1 + x ^{2}}

\int_{2}^{\infty} \frac{1}{4 + x ^{2}} d x

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