integral from 0 to 1 of xe^{-7x^2}

Lösung

\int_{0}^{1} x e^{- 7 x^{2}} d x

\frac{e ^{7} - 1}{14 e ^{7}}

Dezimale

0.07136 \dots

Schritte zur Lösung

\int_{0}^{1} x e^{- 7 x^{2}} d x

Wende U-Substitution an

= \int_{0}^{- 7} - \frac{e ^{u}}{14} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 7}^{0} - \frac{e ^{u}}{14} d u

Entferne die Konstante:

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

= - (- \frac{1}{14} \cdot \int_{- 7}^{0} e^{u} d u)

Nutze das gemeinsame Integral :

\int e^{u} d u = e^{u}

= - (- \frac{1}{14} [e^{u}]_{- 7}^{0})

Vereinfache

= \frac{1}{14} [e^{u}]_{- 7}^{0}

Berechne die Grenzen:

1 - \frac{1}{e ^{7}}

= \frac{1}{14} (1 - \frac{1}{e ^{7}})

Vereinfache

= \frac{e ^{7} - 1}{14 e ^{7}}

\int \frac{e ^{c o s^{2} (x)}}{csc ( 2 x )} d x

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

\int sec^{2} (1) d x

\frac{d}{d θ} (4 sin (3 θ))

(2 x + e^{y}) d x + x e^{y} d y = 0