integral from 0 to 3 of x(e^{x^2}-1)

Lösung

\int_{0}^{3} x (e^{x^{2}} - 1) d x

\frac{e ^{9} - 10}{2}

Dezimale

4046.54196 \dots

Schritte zur Lösung

\int_{0}^{3} x (e^{x^{2}} - 1) d x

Wende U-Substitution an

= \int_{0}^{9} \frac{e ^{u} - 1}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{9} e^{u} - 1 d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int_{0}^{9} e^{u} d u - \int_{0}^{9} 1 d u)

\int_{0}^{9} e^{u} d u = e^{9} - 1

\int_{0}^{9} 1 d u = 9

= \frac{1}{2} (e^{9} - 1 - 9)

Vereinfache

\frac{1}{2} (e^{9} - 1 - 9) : \frac{e ^{9} - 10}{2}

= \frac{e ^{9} - 10}{2}

\int_{0}^{4} 5 (1 - e^{x}) d x

\int_{0}^{7} \frac{1}{( 7 - x ) ^{\frac{4}{3}}} d x

\int_{1}^{3} \frac{( 3 x + 1 ) ^{2}}{x ^{3}} d x

\int_{- 1}^{4} x^{2} + x - 6 d x

\int_{1}^{5} (\frac{3}{x}) d x