integral from 0 to x^2 of f(t)

Lösung

\int_{0}^{x^{2}} f (t) d t

\frac{x ^{4} f}{2}

Schritte zur Lösung

\int_{0}^{x^{2}} f t d t

Entferne die Konstante:

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

= f \cdot \int_{0}^{x^{2}} t d t

Wende die Potenzregel an

= f [\frac{t ^{2}}{2}]_{0}^{x^{2}}

Berechne die Grenzen:

\frac{x ^{4}}{2}

= f \frac{x ^{4}}{2}

Vereinfache

= \frac{x ^{4} f}{2}

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