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

Lösung

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

y^{2} (e - 1)

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{1} e^{u} y^{2} d u

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

= y^{2} [e^{u}]_{0}^{1}

Berechne die Grenzen:

e - 1

= y^{2} (e - 1)

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