integral from-t to t^2 of e^{-x}

Lösung

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

- e^{- t^{2}} + e^{t}

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{t}^{- t^{2}} - e^{u} d u

Entferne die Konstante:

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

= - \int_{t}^{- t^{2}} e^{u} d u

Nutze das gemeinsame Integral :

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

= - [e^{u}]_{t}^{- t^{2}}

Berechne die Grenzen:

e^{- t^{2}} - e^{t}

= - (e^{- t^{2}} - e^{t})

Vereinfache

= - e^{- t^{2}} + e^{t}

\int_{- 1}^{x^{2}} (1 + t^{3})^{4} d t

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\int_{0}^{2} - 2 x^{2} + 4 x d x

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\int_{0}^{1} \frac{1}{x ^{2} + 25} d x