integral from 0 to 25 of sqrt(225-5x)

Lösung

\int_{0}^{25} 225 - 5 x d x

\frac{950}{3}

Dezimale

316.66666 \dots

Schritte zur Lösung

\int_{0}^{25} 225 - 5 x d x

Wende U-Substitution an

= \int_{225}^{100} - \frac{u}{5} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{100}^{225} - \frac{u}{5} d u

Entferne die Konstante:

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

= - (- \frac{1}{5} \cdot \int_{100}^{225} u d u)

Wende die Potenzregel an

= - (- \frac{1}{5} [\frac{2}{3} u^{\frac{3}{2}}]_{100}^{225})

Vereinfache

= \frac{1}{5} [\frac{2}{3} u^{\frac{3}{2}}]_{100}^{225}

Berechne die Grenzen:

\frac{4750}{3}

= \frac{1}{5} \cdot \frac{4750}{3}

Vereinfache

= \frac{950}{3}

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