integral from 0 to 1 of sqrt(1-z)

Lösung

\int_{0}^{1} 1 - z

\frac{2}{3}

Dezimale

0.66666 \dots

Schritte zur Lösung

\int_{0}^{1} 1 - z d z

Wende U-Substitution an

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

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

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

Entferne die Konstante:

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

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

Wende die Potenzregel an

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

Vereinfache

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

Berechne die Grenzen:

\frac{2}{3}

= \frac{2}{3}

\int_{0}^{1} e^{1 - 3 t} d t

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\int_{0}^{2} 2 π x 1 + 4 x^{2} d x