integral from 1 to x of rt^{r-1}

Lösung

\int_{1}^{x} r t^{r - 1} d t

x^{r} - 1

Schritte zur Lösung

\int_{1}^{x} r t^{r - 1} d t

Entferne die Konstante:

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

= r \cdot \int_{1}^{x} t^{- 1 + r} d t

Wende die Potenzregel an

= r [\frac{t ^{r}}{r}]_{1}^{x}

Berechne die Grenzen:

\frac{x ^{r}}{r} - \frac{1}{r}

= r (\frac{x ^{r}}{r} - \frac{1}{r})

Vereinfache

= x^{r} - 1

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

\int_{- π}^{π} x \cdot cos (n x) d x

\int_{s}^{\infty} \frac{1}{s ^{2} + 1} d s

\int_{0}^{1} 11 ln (x) d x

\int_{e}^{e^{2}} x^{2} ln (x) d x