integral from 1 to 3 of 2x^2e^{x^3}

Lösung

\int_{1}^{3} 2 x^{2} e^{x^{3}} d x

\frac{2 ( e ^{27} - e )}{3}

Dezimale

354698827066

Schritte zur Lösung

\int_{1}^{3} 2 x^{2} e^{x^{3}} d x

Entferne die Konstante:

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

= 2 \cdot \int_{1}^{3} x^{2} e^{x^{3}} d x

Wende U-Substitution an

= 2 \cdot \int_{1}^{27} \frac{e ^{u}}{3} d u

Entferne die Konstante:

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

= 2 \cdot \frac{1}{3} \cdot \int_{1}^{27} e^{u} d u

Nutze das gemeinsame Integral :

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

= 2 \cdot \frac{1}{3} [e^{u}]_{1}^{27}

Vereinfache

2 \cdot \frac{1}{3} [e^{u}]_{1}^{27} : \frac{2}{3} [e^{u}]_{1}^{27}

= \frac{2}{3} [e^{u}]_{1}^{27}

Berechne die Grenzen:

e^{27} - e

= \frac{2}{3} (e^{27} - e)

Vereinfache

= \frac{2 ( e ^{27} - e )}{3}

\int_{\frac{π}{3}}^{\frac{π}{2}} ln (sin (x)) d x

\int_{3}^{5} 3 x^{2} d x

\int_{- 7}^{1} x^{4} d x

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

\int_{1}^{3} x^{2} + 4 x d x