integral from 0 to 1 of 5x(x^2-1)^5

Lösung

\int_{0}^{1} 5 x (x^{2} - 1)^{5} d x

- \frac{5}{12}

Dezimale

- 0.41666 \dots

Schritte zur Lösung

\int_{0}^{1} 5 x (x^{2} - 1)^{5} d x

Entferne die Konstante:

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

= 5 \cdot \int_{0}^{1} x (x^{2} - 1)^{5} d x

Wende U-Substitution an

= 5 \cdot \int_{- 1}^{0} \frac{u ^{5}}{2} d u

Entferne die Konstante:

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

= 5 \cdot \frac{1}{2} \cdot \int_{- 1}^{0} u^{5} d u

Wende die Potenzregel an

= 5 \cdot \frac{1}{2} [\frac{u ^{6}}{6}]_{- 1}^{0}

Vereinfache

5 \cdot \frac{1}{2} [\frac{u ^{6}}{6}]_{- 1}^{0} : \frac{5}{2} [\frac{u ^{6}}{6}]_{- 1}^{0}

= \frac{5}{2} [\frac{u ^{6}}{6}]_{- 1}^{0}

Berechne die Grenzen:

- \frac{1}{6}

= \frac{5}{2} (- \frac{1}{6})

Vereinfache

= - \frac{5}{12}

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

\int_{0}^{4} \frac{1}{36 x ^{2} + 49} d x

\int_{0}^{2 π} cos (\frac{x}{2}) d x

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

\int_{0}^{3 x} cos (t) d t