integral from-3 to 0 of 3x^2e^{x^3}

Lösung

\int_{- 3}^{0} 3 x^{2} e^{x^{3}} d x

1 - \frac{1}{e ^{27}}

Dezimale

1

Schritte zur Lösung

\int_{- 3}^{0} 3 x^{2} e^{x^{3}} d x

Entferne die Konstante:

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

= 3 \cdot \int_{- 3}^{0} x^{2} e^{x^{3}} d x

Wende U-Substitution an

= 3 \cdot \int_{- 27}^{0} \frac{e ^{u}}{3} d u

Entferne die Konstante:

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

= 3 \cdot \frac{1}{3} \cdot \int_{- 27}^{0} e^{u} d u

Nutze das gemeinsame Integral :

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

= 3 \cdot \frac{1}{3} [e^{u}]_{- 27}^{0}

Vereinfache

3 \cdot \frac{1}{3} [e^{u}]_{- 27}^{0} : [e^{u}]_{- 27}^{0}

= [e^{u}]_{- 27}^{0}

Berechne die Grenzen:

1 - \frac{1}{e ^{27}}

= 1 - \frac{1}{e ^{27}}

\int_{2}^{x} \frac{3 - t}{2} d t

\int_{- 2}^{x} 100 - t^{4} d t

\int_{1}^{6} - 3 cos (\frac{nπ t}{4}) d t

\int_{\frac{3}{2}}^{6} \frac{x}{2 x - 3} d x

\int_{0}^{2} (9 - x) x d x