integral from 0 to 1 of 2(ax-(x^2+x))

Lösung

\int_{0}^{1} 2 (a x - (x^{2} + x)) d x

a - \frac{5}{3}

Schritte zur Lösung

\int_{0}^{1} 2 (a x - (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_{0}^{1} a x - (x^{2} + x) d x

Wende die Summenregel an:

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

= 2 (\int_{0}^{1} a x d x - \int_{0}^{1} x^{2} + x d x)

\int_{0}^{1} a x d x = \frac{a}{2}

\int_{0}^{1} x^{2} + x d x = \frac{5}{6}

= 2 (\frac{a}{2} - \frac{5}{6})

Vereinfache

2 (\frac{a}{2} - \frac{5}{6}) : a - \frac{5}{3}

= a - \frac{5}{3}

\int_{0}^{1} \frac{4}{3} t^{\frac{3}{2}} (t + 2) d t

\int_{0}^{\infty} x (e^{- x}) d x

\int_{0}^{\frac{π}{2}} 1 - sin^{3} (x) d x

\int_{0}^{1} x^{2} - 1 d x

\int_{0}^{4} ln (3 t + 1) d t