integral from 0 to 1 of (15ln(x))

Lösung

\int_{0}^{1} (15 ln (x)) d x

- 15

Schritte zur Lösung

\int_{0}^{1} 15 ln (x) d x

Entferne die Konstante:

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

= 15 \cdot \int_{0}^{1} ln (x) d x

Wende die partielle Integration an

= 15 [x ln (x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= 15 [x ln (x) - x]_{0}^{1}

Berechne die Grenzen:

- 1

= 15 (- 1)

Vereinfache

= - 15

\int_{2}^{4} 3 x^{2} + 1 d x

\int_{0}^{1} x^{2} + 3 d x

\int_{0}^{1} x^{3} 1 + x^{4} d x

\int_{0}^{r} (b \cdot r^{2} + c \cdot r) 2 π r d r

\int_{0}^{3} x \cdot e^{x} d x