integral from 1 to x of 2x

Lösung

\int_{1}^{x} 2 x d x

x^{2} - 1

Schritte zur Lösung

\int_{1}^{x} 2 x d x

Entferne die Konstante:

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

= 2 \cdot \int_{1}^{x} x d x

Wende die Potenzregel an

= 2 [\frac{x ^{2}}{2}]_{1}^{x}

Berechne die Grenzen:

\frac{x ^{2}}{2} - \frac{1}{2}

= 2 (\frac{x ^{2}}{2} - \frac{1}{2})

Vereinfache

= x^{2} - 1

\int_{- 2 π}^{2 π} x^{2} \cdot sin (2 x) d x

\int_{- 1}^{2} (4 - x^{2}) - (2 - x) d x

\int_{1}^{e} x^{3} ln (3 x) d x

\int_{- 1}^{1} t (7 - t)^{2} d t

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