integral from 0 to 2 of te^{t^2}

Lösung

\int_{0}^{2} t e^{t^{2}} d t

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

Dezimale

26.79907 \dots

Schritte zur Lösung

\int_{0}^{2} t e^{t^{2}} d t

Wende U-Substitution an

= \int_{0}^{4} \frac{e ^{u}}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{4} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [e^{u}]_{0}^{4}

Berechne die Grenzen:

e^{4} - 1

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

Vereinfache

= \frac{e ^{4} - 1}{2}

\frac{\partial}{\partial x} ((2 x - x^{2}) (2 y - y^{2}))

x \to 1 lim (\frac{2 x}{x ^{3} + 1})

2 x y y^{^{'}} = 1 + y^{2}

x \to 0 lim (- 5 (x - 3) ln (x - 3))

y^{^{'}} = 2 (y^{2} + 1)