integral from 0 to 4 of (e^{y^2}y)/2

Lösung

\int_{0}^{4} \frac{e ^{y^{2}} y}{2} d y

\frac{e ^{16} - 1}{4}

Dezimale

2221527.38012 \dots

Schritte zur Lösung

\int_{0}^{4} \frac{e ^{y^{2}} y}{2} d y

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^{y^{2}} y d y

Wende U-Substitution an

= \frac{1}{2} \cdot \int_{0}^{16} \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 \frac{1}{2} \cdot \int_{0}^{16} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} \cdot \frac{1}{2} [e^{u}]_{0}^{16}

Vereinfache

\frac{1}{2} \cdot \frac{1}{2} [e^{u}]_{0}^{16} : \frac{1}{4} [e^{u}]_{0}^{16}

= \frac{1}{4} [e^{u}]_{0}^{16}

Berechne die Grenzen:

e^{16} - 1

= \frac{1}{4} (e^{16} - 1)

Vereinfache

= \frac{e ^{16} - 1}{4}

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