integral from 0 to 1 of-((x-1)^3)/3

Lösung

\int_{0}^{1} - \frac{( x - 1 ) ^{3}}{3} d x

\frac{1}{12}

Dezimale

0.08333 \dots

Schritte zur Lösung

\int_{0}^{1} - \frac{( x - 1 ) ^{3}}{3} d x

Entferne die Konstante:

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

= - \frac{1}{3} \cdot \int_{0}^{1} (x - 1)^{3} d x

Wende U-Substitution an

= - \frac{1}{3} \cdot \int_{- 1}^{0} u^{3} d u

Wende die Potenzregel an

= - \frac{1}{3} [\frac{u ^{4}}{4}]_{- 1}^{0}

Berechne die Grenzen:

- \frac{1}{4}

= - \frac{1}{3} (- \frac{1}{4})

Vereinfache

= \frac{1}{12}

\int_{0}^{1} 2 π (2 - x) (x - x^{2}) d x

\int_{- 4}^{0} (- x^{2} - 4 x) d x

\int_{- 1}^{1} x^{3} - 1 d x

\int_{x}^{- 1} t^{2} + 1 d t

\int_{0}^{2 + y} 1 - 3 z^{2} d z