integral from 0 to a of 1.2xe^{7x^2}

Lösung

\int_{0}^{a} 1.2 x e^{7 x^{2}} d x

0.08571 \dots (e^{7 a^{2}} - 1)

Schritte zur Lösung

\int_{0}^{a} 1.2 x e^{7 x^{2}} d x

Entferne die Konstante:

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

= 1.2 \cdot \int_{0}^{a} x e^{7 x^{2}} d x

Wende U-Substitution an

= 1.2 \cdot \int_{0}^{7 a^{2}} \frac{e ^{u}}{14} d u

Entferne die Konstante:

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

= 1.2 \cdot \frac{1}{14} \cdot \int_{0}^{7 a^{2}} e^{u} d u

Nutze das gemeinsame Integral :

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

= 1.2 \cdot \frac{1}{14} [e^{u}]_{0}^{7 a^{2}}

Vereinfache

1.2 \cdot \frac{1}{14} [e^{u}]_{0}^{7 a^{2}} : 0.08571 \dots [e^{u}]_{0}^{7 a^{2}}

= 0.08571 \dots [e^{u}]_{0}^{7 a^{2}}

Berechne die Grenzen:

e^{7 a^{2}} - 1

= 0.08571 \dots (e^{7 a^{2}} - 1)

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