integral from 0 to 2 of sqrt(1-0.5x)

Lösung

\int_{0}^{2} 1 - 0.5 x d x

\frac{4}{3}

Dezimale

1.33333 \dots

Schritte zur Lösung

\int_{0}^{2} 1 - 0.5 x d x

Wende U-Substitution an

= \int_{1}^{0} - \frac{u}{0.5} d u

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

= - \int_{0}^{1} - \frac{u}{0.5} d u

Entferne die Konstante:

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

= - (- \frac{1}{0.5} \cdot \int_{0}^{1} u d u)

Vereinfache

= - (- 2 \cdot \int_{0}^{1} u d u)

Wende die Potenzregel an

= - (- 2 [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{1})

Vereinfache

= 2 [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{1}

Berechne die Grenzen:

\frac{2}{3}

= 2 \cdot \frac{2}{3}

Vereinfache

= \frac{4}{3}

\int_{0}^{3} \frac{- 2}{5 x + 1} d x

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