integral from 1 to 3 of (2-x)^6

Lösung

\int_{1}^{3} (2 - x)^{6} d x

\frac{2}{7}

Dezimale

0.28571 \dots

Schritte zur Lösung

\int_{1}^{3} (2 - x)^{6} d x

Wende U-Substitution an

= \int_{1}^{- 1} - u^{6} d u

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

= - \int_{- 1}^{1} - u^{6} d u

Entferne die Konstante:

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

= - (- \int_{- 1}^{1} u^{6} d u)

Wende die Potenzregel an

= - (- [\frac{u ^{7}}{7}]_{- 1}^{1})

Vereinfache

= [\frac{u ^{7}}{7}]_{- 1}^{1}

Berechne die Grenzen:

\frac{2}{7}

= \frac{2}{7}

\int_{0}^{2} - x^{2} + 4 x - x^{2} d x

\int_{0}^{2} 2 t^{7} - 6 t^{5} + 4 t d t

\int_{0}^{12} e^{0.1 x} d x

\int_{- 5}^{3} ∣ x + 3 ∣ d x

\int_{1}^{4} (e^{x}) - (\frac{1}{x}) d x