integral from 0 to 7 of 10xln(x)

Lösung

\int_{0}^{7} 10 x ln (x) d x

10 (\frac{49}{2} ln (7) - \frac{49}{4})

Dezimale

354.24798 \dots

Schritte zur Lösung

\int_{0}^{7} 10 x ln (x) d x

Entferne die Konstante:

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

= 10 \cdot \int_{0}^{7} x ln (x) d x

Wende die partielle Integration an

= 10 [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{0}^{7}

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= 10 [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{0}^{7}

Berechne die Grenzen:

\frac{49}{2} ln (7) - \frac{49}{4}

= 10 (\frac{49}{2} ln (7) - \frac{49}{4})

\int_{\frac{π}{6}}^{\frac{π}{2}} 5 cot^{2} (x) d x

\int_{20}^{30} (3 x + 4)^{2} d x

\int_{0}^{\frac{π}{4}} 1 d x

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

\int_{- \infty}^{3} θ e^{θ} d θ